Question

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

Explanation:

Step1: Find the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1=-3,y_1 = - 2,x_2=2,y_2=-7$. So $m=\frac{-7-(-2)}{2-(-3)}=\frac{-7 + 2}{2 + 3}=\frac{-5}{5}=-1$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Let's use the point $( - 3,-2)$ and $m=-1$. Then $y-(-2)=-1(x-(-3))$.

Step3: Simplify the equation

$y + 2=-1(x + 3)$. Expand the right - hand side: $y+2=-x - 3$. Rearrange to the slope - intercept form $y=-x-5$.

Answer:

$y=-x - 5$