Question

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

Explanation:

Step1: Calculate the slope

Given points $(x_1,y_1)=(3,-1)$ and $(x_2,y_2)=(-3,1)$, use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{1-(-1)}{-3-3}=\frac{2}{-6}=-\frac{1}{3}$

Step2: Use point-slope form

Choose point $(3,-1)$, use $y-y_1=m(x-x_1)$
$y-(-1)=-\frac{1}{3}(x-3)$

Step3: Simplify to slope-intercept form

Simplify the equation:
$y+1=-\frac{1}{3}x + 1$
$y=-\frac{1}{3}x$
Alternatively, in standard form: $x + 3y = 0$

Answer:

$y=-\frac{1}{3}x$ (or equivalent standard form $x + 3y = 0$)