Question

Question 7(Multiple Choice Worth 5 points)

(04.07A LC)
Which equation does the graph below represent?
15
12
9
6
3
2 3 4 5
-5 -4 -3 -2 -1 01
31
-6
.9
-12
-15
y =
y = -3x
y = 3x
y = x

Answer 1

`y = -3x`

Explanation:

Given

The attached graph

Required

Determine the graph equation

To do this, we pick any 3 corresponding points of x and y

`(x_1,y_1) = (0,0)`

`(x_2,y_2) = (2,-6)`

`(x_3,y_3) = (-4,12)`

The equation can then be solved using linear interpolation as follows:

`(y-y_3)/(x-x_3) = (y_2 - y_1)/(x_2-x_1)`

This gives:

`(y-12)/(x-(-4)) = (-6 -0)/(2-0)`

`(y-12)/(x+4) = (-6 -0)/(2-0)`

`(y-12)/(x+4) = (-6)/(2)`

`(y-12)/(x+4) = -3`

Multiply both sides by x + 4

`(x + 4) * (y-12)/(x+4) = -3 * (x + 4)`

`y - 12 = -3 *(x + 4)`

Open bracket

`y - 12 = -3x -12`

Add 12 to both sides

`y - 12+12 = -3x -12+12`

`y = -3x`