Question

Examine the graph below.

Select the solutions to the graph from the following points.
Select three that apply.

Answer 1

A. (-15, -5)

C. (3, 2)

E. (21, 8)

Explanation:

From inspection of the graph, two points on the line are:

• (0, 1)
• (-3, 0)

Substitute the two points into the slope formula:

`\textsf{slope}\:(m)=(y_2-y_1)/(x_2-x_1)=(0-1)/(-3-0)=(-1)/(-3)=(1)/(3)`

Substitute the slope and the y-intercept into the slope-intercept formula to create an equation of the line:

`\implies y=(1)/(3)x+1`

To determine which of the given points are solutions to the graph, substitute each x-value into the equation and compare with the the y-value of the solutions.

`x=-15 \implies y=(1)/(3)(-15)+1=-4 \implies (-15,-4)`

`x=-6 \implies y=(1)/(3)(-6)+1=-1 \implies (-6,-1)`

`x=3 \implies y=(1)/(3)(3)+1=2 \implies (3,2)`

`x=12 \implies y=(1)/(3)(12)+1=5 \implies (12,5)`

`x=21 \implies y=(1)/(3)(21)+1=8 \implies (21,8)`

Therefore, the solutions to the graph are:

• A. (-15, -5)
• C. (3, 2)
• E. (21, 8)