what is an equation of the line that passes through the points (-3, -2) and (2, -7)?

Explanation:

Step1: Find the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-3,-2)$ and $(x_2,y_2)=(2,-7)$. Then $m=\frac{-7-(-2)}{2-(-3)}=\frac{-7 + 2}{2 + 3}=\frac{-5}{5}=-1$.

Step2: Use the point - slope form $y - y_1=m(x - x_1)$

Using the point $(-3,-2)$ and $m=-1$, we have $y-(-2)=-1(x - (-3))$.

Step3: Simplify the equation

$y + 2=-1(x + 3)$; expand to get $y+2=-x - 3$; then $y=-x-5$.

Answer:

$y=-x - 5$