Question

a line is graphed in the xy-plane shown. which of the following is an equation of the line?
choose 1 answer:
a $y = \frac{3}{2}x$
b $y = \frac{2}{3}x$
c $y = -\frac{3}{2}x$
d $y = -\frac{2}{3}x$

Explanation:

Step1: Identify slope direction

The line decreases from left to right, so slope $m<0$. Eliminate options A and B.

Step2: Calculate slope using points

Use points $(0,0)$ and $(2,-3)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-3-0}{2-0}=-\frac{3}{2}$

Step3: Confirm line equation

Line passes through origin, so equation is $y=mx$. Substitute $m=-\frac{3}{2}$.

Answer:

C. $y = -\frac{3}{2}x$