what is an equation of the line that passes through the points (-4,1) and (4,-1)?

Explanation:

Step1: Find the slope

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

Step2: Use the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(4,-1)$ and $m =-\frac{1}{4}$, we have $y-(-1)=-\frac{1}{4}(x - 4)$.

Step3: Simplify the equation

$y + 1=-\frac{1}{4}x+1$. Subtract 1 from both sides to get $y=-\frac{1}{4}x$.

Answer:

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