write an equation of the line that passes through the pair of points. (-4, -2), (4, 0)

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-4,-2)$ and $(x_2,y_2)=(4,0)$. Then $m=\frac{0 - (-2)}{4-(-4)}=\frac{2}{8}=\frac{1}{4}$.

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 $m = \frac{1}{4}$, we have $y-0=\frac{1}{4}(x - 4)$.

Step3: Simplify the equation

$y=\frac{1}{4}x-1$.

Answer:

$y=\frac{1}{4}x - 1$