Question

what is an equation of the line that passes through the point (6, -2) and is parallel to the line x - 6y = 12?

Explanation:

Step1: Find slope of given line

Rewrite $x - 6y = 12$ as $y = \frac{1}{6}x - 2$, so slope $m = \frac{1}{6}$.

Step2: Use point-slope form

Point-slope: $y - y_1 = m(x - x_1)$ with $(6, -2)$: $y - (-2) = \frac{1}{6}(x - 6)$

Step3: Simplify to slope-intercept

$y + 2 = \frac{1}{6}x - 1 \implies y = \frac{1}{6}x - 3$

Answer:

$y = \frac{1}{6}x - 3$