what is an equation of the line that passes through the points (0, -8) and (-8, 2)?

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,-8)$ and $(x_2,y_2)=(-8,2)$. Then $m=\frac{2 - (-8)}{-8 - 0}=\frac{10}{-8}=-\frac{5}{4}$.

Step2: Use the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(0,-8)$ (where $x_1 = 0,y_1=-8$) and $m =-\frac{5}{4}$, we get $y-(-8)=-\frac{5}{4}(x - 0)$.

Step3: Simplify the equation

Simplify $y + 8=-\frac{5}{4}x$ to $y=-\frac{5}{4}x-8$.

Answer:

$y =-\frac{5}{4}x - 8$