find an equation of the line that passes through the two given points. write the equation in slope…

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, $x_1=-4,y_1 = 2,x_2 = 4,y_2=-8$. So $m=\frac{-8 - 2}{4-(-4)}=\frac{-10}{8}=-\frac{5}{4}$.

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 $(-4,2)$ and $m =-\frac{5}{4}$. Then $y - 2=-\frac{5}{4}(x+4)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y - 2=-\frac{5}{4}x-5$. Add 2 to both sides to get $y=-\frac{5}{4}x-3$.

Answer:

$y =-\frac{5}{4}x - 3$