Question

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

Explanation:

Step1: Calculate slope of the line

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Using points $(3, -1)$ and $(-3, 1)$:
$m=\frac{1-(-1)}{-3-3}=\frac{2}{-6}=-\frac{1}{3}$

Step2: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Use $(3, -1)$:
$y-(-1)=-\frac{1}{3}(x-3)$

Step3: Simplify to slope-intercept form

Simplify the equation:
$y+1=-\frac{1}{3}x + 1$
$y=-\frac{1}{3}x$

Answer:

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