what is an equation of the line that passes through the points (-8,5) and (-4,0)?

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-8,5)$ and $(x_2,y_2)=(-4,0)$. Then $m=\frac{0 - 5}{-4-(-8)}=\frac{-5}{4}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-4,0)$ and $m =-\frac{5}{4}$, we have $y-0=-\frac{5}{4}(x + 4)$.

Step3: Simplify to slope - intercept form

Expand the right side: $y=-\frac{5}{4}x-5$.

Answer:

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