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Algebra, NAP-K4-CA22

What is the equation for the line shown?
 


 

`y = -3/2 x + 2` `y = 3/2 x + 2` `y = -2/3 x + 2` `y = 2/3 x + 2`
 
 
 
 
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`y = 3/2 x + 2`

Show Worked Solution

`text(Solution 1)`

`text(Graph cuts)\ y text(-axis at 2)`

`text(Gradient) = text(rise)/text(run) = 3/2`

`:. y = 3/2 x + 2`

 

`text(Solution 2)`

`text(Graph passes through)\ (2, 5) and (-2, -1)`

`text(By trial and error:)`

`text(Input each point into option 2’s equation,)`

`5 = 3/2 xx 2 + 2 = 5` ✔

`-1 = 3/2 xx – 2 + 2 = -1` ✔

 
`:. y = 3/2 x + 2\ \ text(is the equation of the line.)“

Algebra, NAP-B4-NC26

Which of these points lies on the straight line joining the points `(4, 6)` and `(16, 12)`?

`(3, 3)` `(5, 5)` `(6, 7)` `(10, 9)`
 
 
 
 
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`(6, 7)`

Show Worked Solution
`text(Gradient)` `= (y_2 – y_1)/(x_2 – x_1)`
  `= (12 – 6)/(16 – 4)`
  `= 6/12`
  `= 1/2`

 

`text(Equation of straight line)`

`m = 1/2,\ text(through)\ (4, 6),`

`y – 6` `= 1/2 (x – 4)`
`y` `= 1/2 x  + 4`

 

`text(Consider)\ (6, 7):`

`7` `= 1/2 xx 6 + 4`
  `= 7`

 

`:. (6, 7)\ text(lies on the line)`

Algebra, NAP-B4-NC18

The coordinates of point `A` are `(7, 5)`.
 

 
`AB` is parallel to the `y`-axis.

If  `AB = 3, BC = 4 and AC = 5`, what are the coordinates of point `C`?

`(3, 2)` `(2, 3)` `(1, 5)` `(5, 1)`
 
 
 
 
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`(3, 2)`

Show Worked Solution

`text(Coordinates of)\ C\ text(are):`

`(7 – 4, 5 – 3) = (3, 2)`

Algebra, NAP-J4-CA22

Leo drew a straight line through the points (0, 5) and (3, −2) as shown in the diagram below. 

What is the gradient of the line that Leo drew?

`7/3` `3/7` `−3/7` `−7/3`
 
 
 
 
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`−7/3`

Show Worked Solution
`text(Gradient)` `= (y_2 – y_1)/(x_2 – x_1)`
  `= (5 – (−2))/(0 – 3)`
  `= −7/3`

Algebra, NAP-D3-NC10

Jeremy sold ice creams out of his ice cream truck.

He drew the graph below to show how the number of ice creams he sells in a week is related to their price.
 

 
Which statement best describes the graph?

 
 As the ice cream price goes up, the number sold goes down.
 
 As the ice cream price goes up, the number sold goes up.
 
 As the ice cream price goes down, the number sold goes down.
 
 As the ice cream price goes down, the number sold stays the same.
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`text(As the ice cream price goes up, the number)`

`text(sold goes down.)`

Show Worked Solution

`text(As the ice cream price goes up, the number)`

`text(sold goes down.)`

Algebra, NAP-H4-NC28

Mal drew the line  `y = 4 - x`  on a grid.

He then drew  `y = x -2`  on the same grid.

What are the coordinates of the intersection point of these two lines?

`(−1,3)` `(1,3)` `(3,−1)` `(3,1)`
 
 
 
 
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`(3,1)`

Show Worked Solution

`text(Strategy one: graph each line and see the intercept.)`

`text(Strategy two:)`

`text(Testing each set of coordinates in both equations,)`

`text{consider the 4th option, (3,1).}`

`1=4-3\ \ text{(satisfies 1st equation)}`

`1=3-2\ \ text{(satisfies 2nd equation)}`

`=>\ (3,1)\ \ text(is the intersection point.)`

Algebra, NAP-H4-CA29

 
Which of these equations represents the line in the graph?

`y = 11 - 2x` `y = 11 + 5.5x` `y = 11 - 5.5x` `y = 11 + 2x`
 
 
 
 
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`y = 11 – 2x`

Show Worked Solution

`text{Graph passes through (0, 11) and (5.5, 0)}`

`text(Gradient)` `=(y_2-y_1)/(x_2-x_1)`  
  `=(11-0)/(0-5.5)`  
  `=-2`  

`:.\ text(Equation is:)\ \ y = 11 – 2x`