what is an equation of the line that passes through the points (-3,8) and (-2,3)?

Explanation:

Step1: Calculate 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, $x_1=-3,y_1 = 8,x_2=-2,y_2 = 3$. So $m=\frac{3 - 8}{-2-(-3)}=\frac{-5}{1}=-5$.

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 $(-2,3)$ and $m=-5$. Then $y - 3=-5(x+2)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y - 3=-5x-10$. Add 3 to both sides to get $y=-5x - 7$.

Answer:

$y=-5x - 7$