Question

question
what is an equation of the line that passes through the points $(-1, 7)$ and $(1, -3)$?

Explanation:

Step1: Calculate slope $m$

Use slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
Substitute $(x_1,y_1)=(-1,7)$ and $(x_2,y_2)=(1,-3)$:
$m=\frac{-3-7}{1-(-1)}=\frac{-10}{2}=-5$

Step2: Use point-slope form

Choose point $(1,-3)$, formula: $y-y_1=m(x-x_1)$
Substitute values:
$y-(-3)=-5(x-1)$

Step3: Simplify to slope-intercept

Expand and rearrange:
$y+3=-5x+5$
$y=-5x+5-3$
$y=-5x+2$

Answer:

$y=-5x+2$