Question

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

Explanation:

Step1: Calculate the slope

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

Step2: Use point-slope form

Point-slope form: $y-y_1=m(x-x_1)$. Use $(-4,1)$ and $m=-\frac{1}{4}$:
$y-1=-\frac{1}{4}(x-(-4))$

Step3: Simplify to slope-intercept form

Simplify the equation:
$y-1=-\frac{1}{4}(x+4)$
$y-1=-\frac{1}{4}x -1$
$y=-\frac{1}{4}x$

Answer:

$y=-\frac{1}{4}x$ (or equivalent forms like $x+4y=0$)