vera wants to graph a line that passes through (0, 2) and has a slope of $\frac{2}{3}$. which points could…

Answer:

A. (-3, 0), D. (3, 4), E. (6, 6)

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $m$ is the slope and $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line. We know that the line passes through $(x_1,y_1)=(0,2)$ and $m = \frac{2}{3}$.

Step2: Check option A

For the point $(-3,0)$: $m=\frac{0 - 2}{-3-0}=\frac{-2}{-3}=\frac{2}{3}$, so $(-3,0)$ is on the line.

Step3: Check option B

For the point $(-2,-3)$: $m=\frac{-3 - 2}{-2-0}=\frac{-5}{-2}=\frac{5}{2}\neq\frac{2}{3}$, so $(-2,-3)$ is not on the line.

Step4: Check option C

For the point $(2,5)$: $m=\frac{5 - 2}{2-0}=\frac{3}{2}\neq\frac{2}{3}$, so $(2,5)$ is not on the line.

Step5: Check option D

For the point $(3,4)$: $m=\frac{4 - 2}{3-0}=\frac{2}{3}$, so $(3,4)$ is on the line.

Step6: Check option E

For the point $(6,6)$: $m=\frac{6 - 2}{6-0}=\frac{4}{6}=\frac{2}{3}$, so $(6,6)$ is on the line.