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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-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`