Question

write the equation of the line
a $y = \frac{2}{3}x - 3$
b $y = -\frac{1}{3}x - 3$
c $y = -3x+\frac{2}{3}$
d $y = -\frac{2}{3}x - 3$

Explanation:

Step1: Find the y - intercept

The line crosses the y - axis at the point $(0, - 3)$, so the y - intercept $b=-3$.

Step2: Find the slope

Use two points on the line, say $(0,-3)$ and $(3, - 5)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-5+3}{3 - 0}=\frac{-2}{3}=-\frac{2}{3}$.

Step3: Write the equation of the line

The slope - intercept form of a line is $y = mx + b$. Substituting $m =-\frac{2}{3}$ and $b=-3$ gives $y=-\frac{2}{3}x - 3$.

Answer:

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