Question

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

Answer 1

Answer:

A.  (-15, -5)

C.  (3, 2)

E.  (21, 8)

Step-by-step explanation:

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

• (0, 1)
• (-3, 0)

Substitute the two points into the slope formula:

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

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

$\implies y=\dfrac{1}{3}x+1$

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.

$x=-15 \implies y=\dfrac{1}{3}(-15)+1=-4 \implies (-15,-4)$

$x=-6 \implies y=\dfrac{1}{3}(-6)+1=-1 \implies (-6,-1)$

$x=3 \implies y=\dfrac{1}{3}(3)+1=2 \implies (3,2)$

$x=12 \implies y=\dfrac{1}{3}(12)+1=5 \implies (12,5)$

$x=21 \implies y=\dfrac{1}{3}(21)+1=8 \implies (21,8)$

Therefore, the solutions to the graph are:

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