Linear Relationships

Linear Relationships, SM-Bank 062

Use the graph of $y=3x-10$ below to find the solution to the equation $3x-10=-1$. (2 marks)

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$x=3$

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$\text{To solve }3x-10=-1\ \text{graphically, find the point}$

$\text{of intersection of the lines }y=-1\ \text{and }y=3x-10$

$\text{i.e. }(3\ ,-1)$

$\therefore\ \text{The solution is }x=3$

Linear Relationships, SM-Bank 061

Use the graph of $y=7-2x$ below to find the solution to the equation $7-2x=-3$. (2 marks)

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$x=5$

Show Worked Solution

$\text{To solve }7-2x=-3\ \text{graphically, find the point}$

$\text{of intersection of the lines }y=-3\ \text{and }y=7-2x$

$\text{i.e. }(5\ ,-3)$

$\therefore\ \text{The solution is }x=5$

Linear Relationships, SM-Bank 060

Use the graph of $y=2x+3$ below to find the solution to the equation $2x+3=11$. (2 marks)

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$x=4$

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$\text{To solve }2x+3=11\ \text{graphically, find the point}$

$\text{of intersection of the lines }y=11\ \text{and }y=2x+3$

$\text{i.e. }(4\ ,\ 11)$

$\therefore\ \text{The solution is }x=4$

Linear Relationships, SM-Bank 059

Verify that the points $(1\ ,\ -1)$ and $(-7 ,\ 3)$ lie on the line $x+2y=-1$? (3 marks)

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$\text{See worked solution}$

Show Worked Solution

$\text{Check points by substituting into }x+2y=-1$

$(1\ ,-1) \longrightarrow$	$LHS$	$=1+2\times (-1)$
		$=1-2=-1$
		$=RHS$

$(-7 ,\ 3) \longrightarrow$	$LHS$	$=-7+2\times 3$
		$=-7+6=-1$
		$=RHS$

$\therefore\ (1\ ,-1)\ \text{and }(-7 ,\ 3) \text{ both lie on the line}\ \ x+2y=-1$

Linear Relationships, SM-Bank 058

Verify that the points $(1\ ,\ 1)$ and $(-2 ,\ 7)$ lie on the line $y=-2x+3$? (3 marks)

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$\text{See worked solution}$

Show Worked Solution

$\text{Check points by substituting into }y=-2x+3$

$(1\ ,\ 1) \longrightarrow$	$RHS$	$=-2\times 1+3$
		$=1$
		$=LHS$

$(-2 ,\ 7) \longrightarrow$	$RHS$	$=-2\times (-2)+3$
		$=7$
		$=LHS$

$\therefore\ (1\ ,\ 1)\ \text{and }(-2 ,\ 7) \text{ both lie on the line}\ \ y=-2x+3$

Linear Relationships, SM-Bank 057

Verify that the points $(2\ ,\ 5)$ and $(-1 ,-1)$ lie on the line $y=2x+1$? (3 marks)

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$\text{See worked solution}$

Show Worked Solution

$\text{Check points by substituting into }y=2x+1$

$(2\ ,\ 5) \longrightarrow$	$RHS$	$=2\times 2+1$
		$=5$
		$=LHS$

$(-1 ,-1) \longrightarrow$	$RHS$	$=2\times (-1)+1$
		$=-1$
		$=LHS$

$\therefore\ (2\ ,\ 5)\ \text{and }(-1 ,-1) \text{ both lie on the line}\ \ y=2x+1$

Linear Relationships, SM-Bank 056 MC

Which of the following points lies on the line $y=2x-4$?

$(0 , 2)$
$(-2 , 8)$
$(2 , -1)$
$(-1, -6)$

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$D$

Show Worked Solution

$\text{Check each option by substituting into }y=2x-4$

$\text{Option A:}\ \ \ $	$2$	$\ne 2\times 0-4=-4$
$\text{Option B:}$	$8$	$\ne 2\times (-2)-4=-8$
$\text{Option C:}$	$-1$	$\ne 2\times 2-4=0$
$\text{Option D:}$	$-6$	$=2\times (-1)-4=-6\ \ \ \checkmark$

$\therefore\ (-1, -6) \text{ lies on the line}\ \ y=2x-4$

$\Rightarrow D$

Linear Relationships, SM-Bank 055 MC

Which of the following points lies on the line $y=10+x$?

$(3 , 7)$
$(-2 , 8)$
$(2 , -8)$
$(-6, -4)$

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$B$

Show Worked Solution

$\text{Check each option by substituting into }y=10+x$

$\text{Option A:}\ \ \ $	$7$	$\ne 10+3$
$\text{Option B:}$	$8$	$=10+-2\ \ \ \checkmark$
$\text{Option C:}$	$-8$	$\ne 10+2$
$\text{Option D:}$	$-4$	$\ne 10+-6$

$\therefore\ (-2, 8) \text{ lies on the line}\ \ y=10+x$

$\Rightarrow B$

Linear Relationships, SM-Bank 054

Renee and Leisa are saving money so they can visit their grandmother on a holiday.

Renee has $100 and plans to save $30 each week.

Leisa has $200 and plans to save $10 each week.

Write an equation to represent
(i) Renee's savings (1 mark)

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(ii) Leisa's savings (1 mark)

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Complete the following tables of values for the equations above. (2 marks)

Renee's savings
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Weeks }(w) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ &\ \ 3\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Savings }(s) \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array}

$\ \ \ \ \ \ \ $

Leisa's savings
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Weeks }(w) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ &\ \ 3\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Savings }(s) \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array}

Using the tables of values, graph both equations on the number plane below. Be sure to extend your lines to the end of the grid. (2 marks)
After how many weeks will Renee and Leisa have saved the same amount? (1 mark)

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a. (i) $s=100+30w$

(ii) $s=200+10w$

$\text{Renee’s savings: }s=100+30w$
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Weeks }(w) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ &\ \ 3\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Savings }(s) \ \rule[-1ex]{0pt}{0pt} & 100 & 130 & 160 & 190\\
\hline
\end{array}

$\ \ \ \ \ \ \ $

$\text{Leisa’s savings: }s=200+10w$
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Weeks }(w) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ &\ \ 3\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Savings }(s) \ \rule[-1ex]{0pt}{0pt} & 200 & 210 & 220 & 230\\
\hline
\end{array}

d. $5\ \text{weeks}$

Show Worked Solution

a. (i) $s=100+30w$

(ii) $s=200+10w$

$\ \ \ \ \ \ \ $

d. $\text{Method 1 – Graphically by inspection}$

$\text{Lines intersect when }w=5\ \text{and }s=$250$

$\text{Method 2 – Algebraically}$

$\text{Solve }s=100+30w\ \text{ and }s=200+10w\ \text{simultaneously}$

$100+30w$	$=200+10w$
$30w-10w$	$=200-100$
$20w$	$=100$
$w$	$=\dfrac{100}{20}=5$

$\therefore\ \text{Amounts are equal after }5 \text{ weeks}.$

Linear Relationships, SM-Bank 053 MC

Paddy and Miffy each bought potatoes from the local farmers' market.

Paddy bought 2 kilograms for $2.50.

Miffy bought 6 kilograms for $7.50.

Which graph best represents the cost of potatoes at the farmers' market?

A.	B.

C.	D.

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$D$

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$\Rightarrow D$

Linear Relationships, SM-Bank 052

Jeremy owns a paddle board hire company. He charges a $20 insurance fee with every hire and $35 for every hour of hire.

Complete the table of values below, where $\large h$ represents the number of hours of hire and $\large w$ represents his total earnings for each hour of hire. (2 marks)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Hours }(h) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 2\ \ &\ \ 4\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Wage }(w) \ \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\end{array}
Write an equation to represent Jeremy's wages, using the variables $h$ and $w$. (1 mark)

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Graph the equation of the line representing Jeremy's wages on the number plane below. Be sure to extend your line to the edge of the grid. (2 marks)
For how many hours would Jeremy have to hire a paddle board to earn $230? (1 mark)

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\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Hours }(h) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 2\ \ &\ \ 4\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Wage }(w) \ \rule[-1ex]{0pt}{0pt} & 20 & 90 & 160 \\
\hline
\end{array}

b. $w=20+35h$

d. $6\ \text{hours}$

Show Worked Solution

a. $\text{Table of values}$

b. $w=20+35h$

d. $\text{Method 1 – Graphically by inspection}$

$\text{When }w=230 , h=6\ \text{hours}$

$\text{Method 2 – Algebraically}$

	$w$	$=20+35h$
	$230$	$=20+35h$
	$35h$	$=230-20$
	$35h$	$=210$
	$h$	$=\dfrac{210}{35}=6$

$\therefore\ \text{Jeremy would have to hire a board for }6\text{ hours to earn } $230.$

Linear Relationships, SM-Bank 051

Julie cleans carpets and upholstery. She charges a $40 call-out fee and $20 for every hour it takes to complete a job.

Complete the table of values below, where $\large h$ represents the number of hours Julie works and $\large w$ represents her total wage. (2 marks)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Hours }(h) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ &\ \ 3\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Wage }(w) \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array}
Write an equation to represent Julie's wages, using the variables $h$ and $w$. (1 mark)

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Graph the equation of the line representing Julie's wages on the number plane below. Be sure to extend your line to the edge of the grid. (2 marks)
For how many hours would Julie have to clean to earn $150? (1 mark)

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\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Hours }(h) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ &\ \ 3\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Wage }(w) \ \rule[-1ex]{0pt}{0pt} & 40 & 60 & 80 & 100 \\
\hline
\end{array}

b. $w=40+20h$

d. $5.5\ \text{hours}$

Show Worked Solution

a. $\text{Table of values}$

b. $w=40+20h$

d. $\text{Method 1 – Graphically by inspection}$

$\text{When }w=150 , h=5.5\ \text{hours}$

$\text{Method 2 – Algebraically}$

	$w$	$=40+20h$
	$150$	$=40+20h$
	$20h$	$=150-40$
	$20h$	$=110$
	$h$	$=\dfrac{110}{20}=5.5$

$\therefore\ \text{Julie would have to work for }5.5\text{ hours to earn } $150.$

Linear Relationships, SM-Bank 050 MC

Which of the following is not true of the lines on the number plane below?

$\text{They have the same }y\text{-intercept}$.
$\text{They both pass through the point}\ (0,-1)$.
$\text{They constant value in the equations of both lines is }-1$.
$\text{They both pass through the point}\ (-1,0)$.

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$D$

Show Worked Solution

$\text{Neither of the lines pass through the point }(-1,0).$

$\Rightarrow D$

Linear Relationships, SM-Bank 049 MC

What do the lines on the following number plane have in common?

$\text{They have the same }y\text{-intercept}$.
$\text{They are parallel to each other}$.
$\text{They both pass through the origin}$.
$\text{They are perpendicular to each other}$.

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$B$

Show Worked Solution

$\text{The lines are parallel}.$

$\Rightarrow B$

Linear Relationships, SM-Bank 048 MC

What do all the lines on the following number plane have in common?

$\text{They all intersect at the point }(2,1)$.
$\text{They are all parallel to each other}$.
$\text{They all intersect at the point }(1,2)$.
$\text{They are all perpendicular to each other}$.

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$C$

Show Worked Solution

$\text{The lines all pass through the point }(1,2).$

$\therefore\ \text{They all intersect at the point }(1,2)$.

$\Rightarrow C$

Linear Relationships, SM-Bank 047

Complete the tables of values below for each given rule. (3 marks)

$y=3-x$
\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -1 &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array}

$y=3x-1$
\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -1 &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array}

On the number plane below, graph the equations from part (a). (2 marks)
Using the graph, find the point of intersection of the two lines. (1 mark)

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c. $(1 , 2)$

Show Worked Solution

c. $\text{Point of intersection: }(1 , 2)$

Linear Relationships, SM-Bank 046 MC

Monique has correctly drawn the graph of $y=-2x+5$ on the number plane below.

She used the points $(-1,7),\ (0,5)$ and $(1,3)$ to draw the line.

How many more different points could she have used to plot the line $y=-2x+5$?

$0$
$2$
$8$
$\text{An infinite number}$

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$D$

Show Worked Solution

$\text{Straight lines are made up of an infinite number of points.}$

$\Rightarrow D$

Linear Relationships, SM Bank 045

Complete the tables of values below for each given rule. (3 marks)

$y=2x+1$
\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -1 &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array}

$y=x-2$
\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -1 &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array}

On the number plane below, graph the equations from part (a). (2 marks)
Using the graph, find the point of intersection of the two lines. (1 mark)

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c. $(-3 , -5)$

Show Worked Solution

c. $\text{Point of intersection: }(-3 , -5)$

Linear Relationships, SM-Bank 044

Complete the table of values using the graph of the straight line below. (2 marks)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -2 & -1 &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & & & & & \\
\hline
\end{array}
Using either the table or the graph, state the rule connecting $\large x$ and $\large y$. (1 mark)

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\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -2 & -1 &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & 3 & 2 & 1 & 0 & -1 \\
\hline
\end{array}

b. $y=-x+1$

Show Worked Solution

a. $\text{Table of values}$

b. $\text{The }y\ \text{values are decreasing by } 1\ \text{and when }x=0,\ \ y=1$

$\therefore\ \text{Rule: }y=-x+1$

Linear Relationships, SM-Bank 043

Complete the table of values using the graph of the straight line below. (2 marks)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -2 & -1 &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & & & & & \\
\hline
\end{array}
Using either the table or the graph, state the rule connecting $\large x$ and $\large y$. (1 mark)

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b. $y=2x+1$

Show Worked Solution

a. $\text{Table of values}$

b. $\text{The }y\ \text{values are increasing by } 2\ \text{and when }x=0,\ \ y=1$

$\therefore\ \text{Rule: }y=2x+1$

Linear Relationships, SM-Bank 042

Plot the points from the table on the number plane below and join the points using a ruler. (2 marks)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -2 & -1 &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & 2 & 2 & 2 & 2 & 2\\
\hline
\end{array}
What do you notice about the points? (1 mark)

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Using either the table or the graph, state the rule connecting $\large x$ and $\large y$. (1 mark)

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b. $\text{They form a horizontal straight line.}$

c. $y=2$

Show Worked Solution

b. $\text{They form a horizontal straight line.}$

\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} &\ \ -2\ \ &\ \ -1\ \ &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & 2 & 2 & 2 & 2 & 2\\
\hline
\end{array}

$y=2\text{ regardless of the value of }x$

$\therefore\ \text{Rule: }y=2$

Linear Relationships, SM-Bank 041

Plot the points from the table on the number plane below and join the points using a ruler. (2 marks)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} &\ \ -2\ \ &\ \ -1\ \ &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & 5 & 4 & 3 & 2 & 1\\
\hline
\end{array}
What do you notice about the points? (1 mark)

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Using either the table or the graph, state the rule connecting $\large x$ and $\large y$. (1 mark)

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b. $\text{They form a straight line.}$

c. $y=3-x$

Show Worked Solution

b. $\text{They form a straight line.}$

$\therefore\ \text{Rule: }y=3-x$

Linear Relationships, SM-Bank 040

Plot the points from the table on the number plane below and join the points using a ruler. (2 marks)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} &\ \ -2\ \ &\ \ -1\ \ &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & -4 & -2 & 0 & 2 & 4\\
\hline
\end{array}
What do you notice about the points? (1 mark)

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Using either the table or the graph, state the rule connecting $\large x$ and $\large y$. (1 mark)

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b. $\text{They form a straight line.}$

c. $y=2x$

Show Worked Solution

b. $\text{They form a straight line.}$

$\therefore\ \text{Rule: }y=2x$

Linear Relationships, SM-Bank 039 MC

Pepper uses matchsticks to make a pattern of shapes, as shown in the table below.

The equation used to show the relationship between $T$ and $N$ is

$T = N + 1$
$T = 6N$
$T = 6N+2$
$T = 6N-4$

Show Answers Only

$D$

Show Worked Solution

$T\ \text{increases by 6 each shape.}$

$\text{Consider}\ T = 6N – 4:$

$\text{When}\ \ N = 1,\ T = 6\times 1 − 4 = 2$

$\text{When}\ \ N = 2, \ T = 6\times − 4 = 8$

$\text{When}\ \ N = 3,\ T = 6\times − 4 = 14$

$\therefore T = 6N − 4\ \text{is correct}$

$\Rightarrow D$

Linear Relationships, SM-Bank 038

Complete the table of values below for the rule $ y=4x-7$. (2 marks)

\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -1 &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array}
Use the table to list the coordinates of the points. (2 marks)

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a. $\text{Table of values}$

\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt}& -1 &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & -11 & -7 & -3 & 1\\
\hline
\end{array}

b. $(-1 , -11)\ \ (0 , -7)\ \ (1 , -3)\ \ (2 , 1)$

Show Worked Solution

a. $\text{Table of values}$

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} &\ \ -1\ \ &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & 4\times (-1)-7=-11 & 4\times (0)-7=-7 & 4\times 1-7=-3 &4\times 2-7=1\\
\hline
\end{array}

b. $(-1 , -11)\ \ (0 , -7)\ \ (1 , -3)\ \ (2 , 1)$

Linear Relationships, SM-Bank 037

Complete the table of values below for the rule $ y=5-x$. (2 marks)

\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -1 &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array}
Use the table to list the coordinates of the points. (2 marks)

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a. $\text{Table of values}$

\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt}& -1 &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & 6 & 5 & 4 & 3\\
\hline
\end{array}

b. $(-1 , 6)\ \ (0 , 5)\ \ (1 , 4)\ \ (2 , 3)$

Show Worked Solution

a. $\text{Table of values}$

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} &\ \ -1\ \ &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & 5-(-1)=6 & 5-0=5 & 5-1=4 & 5-2=3\\
\hline
\end{array}

b. $(-1 , 6)\ \ (0 , 5)\ \ (1 , 4)\ \ (2 , 3)$

Linear Relationships, SM-Bank 036

Complete the table of values below for the given rule. (2 marks)

$ v=4u-3$

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ u\ \ \rule[-1ex]{0pt}{0pt} & -2 & -1 &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ v\ \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array}

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Show Worked Solution

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ u\ \ \rule[-1ex]{0pt}{0pt} &\ \ -2\ \ &\ \ -1\ \ &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ v\ \ \rule[-1ex]{0pt}{0pt} & 4\times -2-3=-11 & 4\times -1-3=-7 & 4\times 0-3=-3 & 4\times 1-3=1 & 4\times 2-3=5\\
\hline
\end{array}

Linear Relationships, SM-Bank 035

Complete the table of values below for the given rule. (2 marks)

$ y=-x$

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} & -2 & -1 &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array}

--- 0 WORK AREA LINES (style=lined) ---

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Show Worked Solution

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} &\ \ -2\ \ &\ \ -1\ \ &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & -(-2)=2 & -(-1)=1 & -(0)=0 & -(1)=-1 & -(2)=-2\\
\hline
\end{array}

Linear Relationships, SM-Bank 034

Complete the table of values below for the given rule. (2 marks)

$ y=2x+1$

\begin{array} {|l|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} &\ \ -2\ \ &\ \ -1\ \ &\ \ 0\ \ &\ \ 1\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array}

--- 0 WORK AREA LINES (style=lined) ---

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Linear Relationships, SM-Bank 033

Complete the table of values below for the given rule. (2 marks)

$ y=2+x$

\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\ \ x\ \ \rule[-1ex]{0pt}{0pt} &\ \ 1\ \ &\ \ 2\ \ &\ \ 3\ \ &\ \ 4\ \ \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array}

--- 0 WORK AREA LINES (style=lined) ---

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Linear Relationships, SM-Bank 032 MC

Which rule correctly describes the pattern below?

$\text{The number of pins}=2\times \text{The number of squares}+3$
$\text{The number of pins}=3\times \text{The number of squares}+1$
$\text{The number of pins}=1\times \text{The number of squares}+3$
$\text{The number of pins}=4\times \text{The number of squares}$

Show Answers Only

$B$

Show Worked Solution

\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \text{Number of squares} \rule[-1ex]{0pt}{0pt} & 1 & 2 & 3 \\
\hline
\rule{0pt}{2.5ex} \text{Number of pins} \rule[-1ex]{0pt}{0pt} & 4 & 7 & 10 \\
\hline
\end{array}

$\therefore\ \text{The number of pins}=3\times \text{Number of squares}+1$

$\Rightarrow B$

Linear Relationships, SM-Bank 031 MC

Which rule correctly describes the pattern below?

$\text{The number of pins}=\text{The number of triangles}+3$
$\text{The number of pins}=\text{The number of triangles}+5$
$\text{The number of pins}=\text{The number of triangles}\times 2$
$\text{The number of pins}=\text{The number of triangles}\times 3$

Show Answers Only

$D$

Show Worked Solution

$\text{Number of triangles }(t)$	$\ \ 1\ \ $	$\ \ 2\ \ $	$\ \ 3\ \ $	$\ \ ….\ \ $
$\text{Number of pins }(p)$	$\ \ 3\ \ $	$\ \ 6\ \ $	$\ \ 9\ \ $	$\ \ ….\ \ $

$\therefore\ \text{The number of pins}=\text{Number of triangles}\times 3$

$\Rightarrow D$

Linear Relationships, SM-Bank 030

Michael is making a geometric pattern using sticks to make pentagons.

The first 3 shapes in the pattern are shown below.

Draw the next shape in the pattern. (1 mark)

--- 6 WORK AREA LINES (style=lined) ---
Complete the table of values using the pattern. (2 marks)

Number of pentagons $(\large p)$ $\ \ 1\ \ $ $\ \ 2\ \ $ $\ \ 3\ \ $ $\ \ 4\ \ $

Number of sticks $(\large s)$ $\ \ 5\ \ $
Write the rule connecting the number of sticks $(s)$ to the number of pentagons $(p)$. (2 marks)

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How many sticks will be needed to make $12$ pentagons? (2 marks)

--- 3 WORK AREA LINES (style=lined) ---

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a. $\text{Shape number }4$

b. $\text{Table of values}$

$\text{Number of pentagons }(\large p)$	$\ \ 1\ \ $	$\ \ 2\ \ $	$\ \ 3\ \ $	$\ \ 4\ \ $
$\text{Number of sticks }(\large s)$	$\ \ 5\ \ $	$\ \ 9\ \ $	$\ \ 13\ \ $	$\ \ 17\ \ $

c. $s=4\times p+1$

d. $49$

Show Worked Solution

a. $\text{Shape number }4$

b. $\text{Table of values}$

$\text{Number of pentagons }(\large p)$	$\ \ 1\ \ $	$\ \ 2\ \ $	$\ \ 3\ \ $	$\ \ 4\ \ $
$\text{Number of sticks }(\large s)$	$\ \ 5\ \ $	$\ \ 9\ \ $	$\ \ 13\ \ $	$\ \ 17\ \ $

c. $\text{Rule: The number of sticks}=4\times \text{(the number of pentagons)}+1$

$\therefore\ \text{Rule: }\ s=4\times p+1$

d. $\text{Find the value of }s\ \text{when }p=12$

$s=4\times p+1=4\times 12+1=49$

Linear Relationships, SM-Bank 029

Michael is making a geometric pattern using pins to form triangles.

The first 3 shapes in the pattern are shown below.

Draw the next shape in the pattern. (1 mark)

--- 6 WORK AREA LINES (style=lined) ---
Complete the table of values using the pattern. (2 marks)

Number of triangles $(t)$ $\ \ 1\ \ $ $\ \ 2\ \ $ $\ \ 3\ \ $ $\ \ 4\ \ $

Number of pins $(p)$ $\ \ 3\ \ $
Write the rule connecting the number of pins $(p)$ to the number of triangles $(t)$. (2 marks)

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How many pins will be needed to make $25$ triangles? (2 marks)

--- 2 WORK AREA LINES (style=lined) ---

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a. $\text{Shape number }4$

b. $\text{Table of values}$

$\text{Number of triangles }(t)$	$\ \ 1\ \ $	$\ \ 2\ \ $	$\ \ 3\ \ $	$\ \ 4\ \ $
$\text{Number of pins }(p)$	$\ \ 3\ \ $	$\ \ 5\ \ $	$\ \ 7\ \ $	$\ \ 9\ \ $

c. $p=2\times t+1$

d. $51$

Show Worked Solution

a. $\text{Shape number }4$

b. $\text{Table of values}$

$\text{Number of triangles }(t)$	$\ \ 1\ \ $	$\ \ 2\ \ $	$\ \ 3\ \ $	$\ \ 4\ \ $
$\text{Number of pins }(p)$	$\ \ 3\ \ $	$\ \ 5\ \ $	$\ \ 7\ \ $	$\ \ 9\ \ $

c. $\text{Rule: The number of pins}=2\times \text{(the number of triangles)}+1$

$\therefore\ \text{Rule: }\ p=2\times t+1$

d. $\text{Find the value of }p\ \text{when }t=25$

$p=2\times t+1=2\times 25+1=51$

Linear Relationships, SM-Bank 028

A weekly gym membership can be purchased for different numbers of classes, as shown in the table below.

Number of classes	1	2	3	4
Cost in dollars	42	72	102	132

What is the rule connecting the number of classes purchased and the cost in dollars? (2 marks)

Show Answers Only

$\text{Cost in dollars}=30\times \text{Number of classes}+12$

Show Worked Solution

$\text{Firstly, look at the increase in the cost with each additional class }$

$\longrightarrow\ 42 , 72 , 102 , 132\ \ \longrightarrow\text{The cost increases by }$30\text{ every class}$

$\text{Secondly, if we look at the difference between }42\ \text{and }30\ \text{in the first class}$

$\text{we get }12\text{ which needs to be added to each membership}$

$\therefore\ \text{Rule: Cost in dollars}=30\times \text{Number of classes}+12$

Linear Relationships, SM-Bank 027

A surfboard can be hired for different numbers of hours, as shown in the table below.

Number of hours	1	2	3	4
Cost in dollars	35	50	65	80

What is the rule connecting the number of hours of surfboard hire and the cost in dollars? (2 marks)

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$ Cost in dollars}=15\times \text{Number of hours}+20$

Show Worked Solution

$\text{Firstly, look at the increase in the cost with each hour of hire }$

$\longrightarrow\ 35 , 50 , 65 , 80\ \ \longrightarrow\text{The price increases by }$15\text{ every hour}$

$\text{Secondly, if we look at the difference between }35\ \text{and }15\ \text{in the first hour}$

$\text{we get }20\text{ which needs to be added to each hiring fee}$

$\therefore\ \text{Rule: Cost in dollars}=15\times \text{Number of hours}+20$

Linear Relationships, SM-Bank 026 MC

Dress sizes
Country A	6	8	10	12	14
Country B	36	38	40	42	44

What is the rule connecting dress sizes in Country A and Country B?

$\text{Country B}=\text{Country A}-30$
$\text{Country B}=\text{Country A}+30$
$\text{Country B}=(4\times\text{Country A})+12$
$\text{Country B}=6\times\text{Country A}$

Show Answers Only

$B$

Show Worked Solution

$\text{Rule: Country B = Country A + 30}$

$\Rightarrow B$

Linear Relationships, SM-Bank 025 MC

Billy is setting up tables for a comedy night at his club.

An X is placed for every available seat at a table, as shown below.

Which of these rules can be used to work out how many people can sit on any row of tables?

$\text{number of tables}\times 6$
$\text{number of tables}\ ÷\ 2-2$
$\text{number of tables}\times 4+2$
$\text{number of tables}\times 4-2$

Show Answers Only

$C$

Show Worked Solution

$\text{Consider Option C:}$

$\text{1st table:}\ \ 1\times 4 +2 = 6\ \text{people}$

$\text{2nd table:}\ \ 2\times 4 +2 = 10\ \text{people}$

$\text{3rd table:}\ \ 3\times 4 +2 = 14\ \text{people}$

$\therefore\ \text{number of tables}\times 4 + 2\ \text{is the correct rule.}$

$\Rightarrow C$

Linear Relationships, SM-Bank 024

The table below has a pattern. The top and bottom numbers are connected by a rule.

Top Number	$1$	$2$	$3$	$4$
Bottom Number	$0$	$-1$	$-2$	$-3$

What is the rule connecting the top number and the bottom number? (2 marks)

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What is the bottom number when the top number is $21$? (2 marks)

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a. $\text{Bottom number}=\text{Top number}\ ÷ \ 3$

b. $-2$

Show Worked Solution

Top Number	$1$	$2$	$3$	$4$
Bottom Number	$1-1=0$	$1-2=-1$	$1-3=-2$	$1-4=-3$

$\text{Rule: Bottom number}=1-\text{Top number}$

b. $\text{Bottom number}=1-\text{Top number}=1-21=-20$

Linear Relationships, SM-Bank 023

The table below has a pattern. The top and bottom numbers are connected by a rule.

Top Number	21	18	15	12
Bottom Number	7	6	5	4

What is the rule connecting the top number and the bottom number? (2 marks)

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What is the bottom number when the top number is $-6$? (2 marks)

--- 2 WORK AREA LINES (style=lined) ---

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a. $\text{Bottom number}=\text{Top number}\ ÷ \ 3$

b. $-2$

Show Worked Solution

Top Number	$21$	$18$	$15$	$12$
Bottom Number	$21\ ÷\ 3=7$	$18\ ÷\ 3=6$	$15\ ÷\ 3=5$	$12\ ÷\ 3=4$

$\text{Rule: Bottom number}=\text{Top number}\ ÷\ 3$

b. $\text{Bottom number}=\text{Top number}\ ÷\ 3=-6\ ÷\ 3=-2$

Linear Relationships, SM-Bank 022

The table below has a pattern. The top and bottom numbers are connected by a rule.

Top Number	2	4	6	8
Bottom Number	8	16	24	32

What is the rule connecting the top number and the bottom number? (2 marks)

--- 2 WORK AREA LINES (style=lined) ---
What is the bottom number when the top number is 15? (2 marks)

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a. $\text{Bottom number}=4\times \text{Top number}$

b. $60$

Show Worked Solution

Top Number	$2$	$4$	$6$	$8$
Bottom Number	$4\times 2=8$	$4\times 4=16$	$4\times 6=24$	$4\times 8=32$

$\text{Rule: Bottom number}=4\times \text{Top number}$

b. $\text{Rule: Bottom number}=4\times \text{Top number}=4\times 15=60$

Linear Relationships, SM-Bank 022

Sabre is saving to buy a new skateboard.

After one week she has saved $11.

She then saves the same amount of money each week.

Week	1	2	3	4
Total Amount Saved	$11	$18	$25	$32

State the rule linking the week and the total amount saved. (2 marks)

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How much money will Sabre have saved by the end of week 10? (2 marks)

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a. $\text{Rule: Amount saved}=$4 + \text{week}\times 7$

b. $$74$

Show Worked Solution

a. $\text{Total at end of week }1= $11$

$\therefore\ \text{After week 1 savings increase by }$7\ \text{per week}$

$\therefore\ \text{Total at end of week 2}=$4 + 2\times 7= $18$

$\therefore\ \text{Total at end of week 3}=$4 + 3\times 7= $25$

$\therefore\ \text{Total at end of week 4}=$4 + 4\times 7= $32$

$\therefore\ \text{Rule: Amount saved}=$4 + \text{week}\times 7$

b. $\text{Total savings at end of week}\ 10$

$= 4 + 10\times 7$

$= $74$

Linear Relationships, SM-Bank 020 MC

Jerry's wage is calculated using an amount per hour plus a travel allowance.

This table shows some of Jerry's wage amounts.

Hours	1	2	3	4
Wage	$85	$140	$195	$250

How are Jerry's wages calculated?

$40 per hour + $35 travel allowance
$60 per hour + $25 travel allowance
$55 per hour + $30 travel allowance
$45 per hour + $40 travel allowance

Show Answers Only

$C$

Show Worked Solution

$\text{Testing Option C equation with the table values:}$

$85$	$=1\times 55+30\ \ \checkmark$
$140$	$=2\times 55+30\ \ \checkmark$
$195$	$=3\times 55+30\ \ \checkmark$
$250$	$=4\times 55+30\ \ \checkmark$

$\Rightarrow C$

Linear Relationships, SM-Bank 019 MC

A plumber calculates the price of a job using a service fee and an amount per hour.

This table shows some of the job prices.

Hours	1	2	3	4
Job price	$90	$130	$170	$210

How are the jobs calculated?

$50 service fee + $40 per hour
$58 service fee + $32 per hour
$60 service fee + $30 per hour
$70 service fee + $20 per hour

Show Answers Only

$A$

Show Worked Solution

$\text{Testing Option A equation with the table values:}$

$90$	$= 50 + 1\times 40\ \ \checkmark$
$130$	$= 50 + 2\times 40\ \ \checkmark$
$170$	$= 50 + 3\times 40\ \ \checkmark$
$210$	$= 50 + 4\times 40\ \ \checkmark$

$\Rightarrow A$

Linear Relationships, SM-Bank 018 MC

Jennifer had 20 cupcakes for sale at the beginning of the day. The table shows the number of cupcakes at the beginning of each hour.

Hour	0	1	2	3
Cupcakes	20	16	12	8

The table also shows a pattern in the number of cupcakes sold. The correct pattern connecting the hour and the number of cupcakes is:

$20-\text{Hour}\times 1$
$20-\text{Hour}\times 4$
$20+\text{Hour}\times 2$
$19+\text{Hour}$

Show Answers Only

$B$

Show Worked Solution

$\text{Consider Option B }:\ 20-\text{Hour}\times 4$

$\text{Hour 0}\longrightarrow$	$20-4\times 0=20$	$\checkmark$
$\text{Hour 1}\longrightarrow$	$20-4\times 1=16$	$\checkmark$
$\text{Hour 2}\longrightarrow$	$20-4\times 2=12$	$\checkmark$
$\text{Hour 3}\longrightarrow$	$20-4\times 3=8$	$\checkmark$

$\Rightarrow B$

Linear Relationships, SM-Bank 017 MC

This table shows the growth of a plant, in centimetres, over a 4 week period.

Week	1	2	3	4
Growth (cm)	3	4	5	6

The table also shows a pattern in the growth of the plant. The correct pattern connecting the week and the growth is:

$\text{Week}\times 3$
$\text{Week}\times 4-1$
$\text{Week}\times 2+1$
$\text{Week}+2$

Show Answers Only

$D$

Show Worked Solution

$\text{Consider Option D }:\ \text{Week}+2$

$\text{Week 1}\longrightarrow$	$1+2=3$	$\checkmark$
$\text{Week 2}\longrightarrow$	$2+2=4$	$\checkmark$
$\text{Week 3}\longrightarrow$	$3+2=5$	$\checkmark$
$\text{Week 4}\longrightarrow$	$4+2=6$	$\checkmark$

$\Rightarrow D$

Linear Relationships, SM-Bank 016 MC

This chart shows the longest run, in kilometres, that Deek ran each week over 4 weeks.

Week	1	2	3	4
Longest Run (km)	8	11	14	17

The chart also shows a pattern in Deek's running. The correct pattern connecting the week and the longest run is:

$\text{Week}\times 8$
$\text{Week}\times 2+6$
$\text{Week}\times 3+5$
$\text{Week}+7$

Show Answers Only

$C$

Show Worked Solution

$\text{Consider Option C }:\ \text{Week}\times 3+5$

$\text{Week 1}\longrightarrow$	$1\times 3+5=8$	$\checkmark$
$\text{Week 2}\longrightarrow$	$2\times 3+5=11$	$\checkmark$
$\text{Week 3}\longrightarrow$	$3\times 3+5=14$	$\checkmark$
$\text{Week 4}\longrightarrow$	$4\times 3+5=17$	$\checkmark$

$\Rightarrow C$

Linear Relationships, SM-Bank 015 MC

The table below has a pattern. The top and bottom numbers are connected by a rule.

\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Top number} \rule[-1ex]{0pt}{0pt} &\ \ 1\ \ &\ \ 2\ \ &\ \ 3\ \ &\ \ 4\ \ & \ldots &\ \ ?\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Bottom number} \rule[-1ex]{0pt}{0pt} & 3 & 6 & 9 & 12 & \ldots & 27 \\
\hline
\end{array}

What is the top number when the bottom number is 27?

$5$
$6$
$9$
$19$

Show Answers Only

$C$

Show Worked Solution

$\text{Top number}\times 3 =\ \text{Bottom number}$

$\text{Top number}\times 3 = 27$

$\therefore\ \text{Top number}\ = \dfrac{27}{3}=9$

$\Rightarrow C$

Linear Relationships, SM-Bank 014 MC

The table below has a pattern. The top and bottom numbers are connected by a rule.

\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \text{Top Number} \rule[-1ex]{0pt}{0pt} & 1 & 2 & 3 & 4 & ... & ? \\
\hline
\rule{0pt}{2.5ex} \text{Bottom Number} \rule[-1ex]{0pt}{0pt} & 4 & 8 & 12 & 16 & ... & 28 \\
\hline
\end{array}

What is the top number when the bottom number is 28?

$5$
$7$
$12$
$17$

Show Answers Only

$B$

Show Worked Solution

$\text{Top number}\ \times 4 =\ \text{Bottom number}$

$\text{Top number}\ \times 4 = 28$

$\therefore\ \text{Top number}\ = \dfrac{28}{4}=7$

$\Rightarrow B$

Linear Relationships, SM-Bank 013

Plot and label the following points on the grid below. (2 marks)

$A(-2.5 , -1.5)\ \ B(1.5 , 0)\ \ C(4.5 , -2)\ \ D(-1.25, 2)$

--- 0 WORK AREA LINES (style=lined) ---

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Show Worked Solution

Linear Relationships, SM-Bank 012

Christian draws a triangle on a number plane as shown below.

What are the coordinates of the point at vertex $C$? (1 mark)

Show Answers Only

$C(-4 , -3)$

Show Worked Solution

$\text{Coordinates are: }\ C(-4 , -3)$

Linear Relationships, SM-Bank 011

Karl draws a rectangle on a number plane as shown below.

What are the coordinates of the point $D$? (1 mark)

Show Answers Only

$(3 , -4)$

Show Worked Solution

$\text{Coordinates are: }\ D(3 , -4)$

Linear Relationships, SM-Bank 010

Plot and label the following points on the grid below. (2 marks)

$A(-3 , 3)\ \ B(4 , 0)\ \ C(3 , -2)\ \ D(-4, -2)$

--- 0 WORK AREA LINES (style=lined) ---

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Linear Relationships, SM-Bank 009

Plot and label the following points on the grid below. (2 marks)

$A(2 , 3)\ \ B(-1 , -4)\ \ C(-2 , 1)\ \ D(0, -1)$

--- 0 WORK AREA LINES (style=lined) ---

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Linear Relationships, SM-Bank 008 MC

The co-ordinates of the point $R$ are:

$(0 , -3)$
$(-3 , 0)$
$(-3 , -3)$
$(0 , -3.5)$

Show Answers Only

$A$

Show Worked Solution

$\text{Coordinates are: }\ (0 , -3)$

$\Rightarrow A$

Linear Relationships, SM-Bank 007 MC

The co-ordinates of the point $Q$ are:

$(2 , 2)$
$(2 , 0)$
$(0 , 2)$
$(2, 1)$

Show Answers Only

$B$

Show Worked Solution

$\text{Coordinates are: }\ (2 , 0)$

$\Rightarrow B$

Linear Relationships, SM_Bank 006 MC

The co-ordinates of the point $P$ are:

$(3\dfrac{1}{2} , -3\dfrac{1}{2})$
$(4\dfrac{1}{2} , -2\dfrac{1}{2} )$
$(-3\dfrac{1}{2} , -4\dfrac{1}{2} )$
$(3\dfrac{1}{2}, -2\dfrac{1}{2} )$

Show Answers Only

$D$

Show Worked Solution

$\text{Coordinates are: }\ (3\dfrac{1}{2} , -2\dfrac{1}{2})$

$\Rightarrow D$

Linear Relationships, SM-Bank 005 MC

The co-ordinates of the point $X$ are:

$(-3.5 , -4 )$
$(-2.5 , -4 )$
$(-4 , -2.5 )$
$(-4, -3.5 )$

Show Answers Only

$B$

Show Worked Solution

$\text{Coordinates are: }\ (-2.5 , -4)$

$\Rightarrow B$

Linear Relationships, SM-Bank 004 MC

The co-ordinates of the point $C$ are:

$(4 , 2 )$
$(2 , 4 )$
$(-4 , 2 )$
$(-2, -4 )$

Show Answers Only

$A$

Show Worked Solution

$\text{Coordinates are: }\ (4 , 2)$

$\Rightarrow A$

Linear Relationships, SM-Bank 003 MC

The co-ordinates of the point $A$ are:

$(-2 , 3 )$
$(-2 , -3 )$
$(-3 , 2 )$
$(3, -2 )$

Show Answers Only

$B$

Show Worked Solution

$\text{Coordinates are: }\ (-2 , -3)$

$\Rightarrow B$

\((1\ ,-1) \longrightarrow\)	\(LHS\)	\(=1+2\times (-1)\)
		\(=1-2=-1\)
		\(=RHS\)

\((-7 ,\ 3) \longrightarrow\)	\(LHS\)	\(=-7+2\times 3\)
		\(=-7+6=-1\)
		\(=RHS\)

\((1\ ,\ 1) \longrightarrow\)	\(RHS\)	\(=-2\times 1+3\)
		\(=1\)
		\(=LHS\)

\((-2 ,\ 7) \longrightarrow\)	\(RHS\)	\(=-2\times (-2)+3\)
		\(=7\)
		\(=LHS\)

\((2\ ,\ 5) \longrightarrow\)	\(RHS\)	\(=2\times 2+1\)
		\(=5\)
		\(=LHS\)

\(\text{Option A:}\ \ \ \)	\(2\)	\(\ne 2\times 0-4=-4\)
\(\text{Option B:}\)	\(8\)	\(\ne 2\times (-2)-4=-8\)
\(\text{Option C:}\)	\(-1\)	\(\ne 2\times 2-4=0\)
\(\text{Option D:}\)	\(-6\)	\(=2\times (-1)-4=-6\ \ \ \checkmark\)

\(\text{Option A:}\ \ \ \)	\(7\)	\(\ne 10+3\)
\(\text{Option B:}\)	\(8\)	\(=10+-2\ \ \ \checkmark\)
\(\text{Option C:}\)	\(-8\)	\(\ne 10+2\)
\(\text{Option D:}\)	\(-4\)	\(\ne 10+-6\)

\(100+30w\)	\(=200+10w\)
\(30w-10w\)	\(=200-100\)
\(20w\)	\(=100\)
\(w\)	\(=\dfrac{100}{20}=5\)

	\(w\)	\(=20+35h\)
	\(230\)	\(=20+35h\)
	\(35h\)	\(=230-20\)
	\(35h\)	\(=210\)
	\(h\)	\(=\dfrac{210}{35}=6\)