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: Convert to slope-intercept form

Rewrite $x - 6y = 12$ to $y = mx + b$:

$$\begin{align*} -6y &= -x + 12\\ y &= \frac{1}{6}x - 2 \end{align*}$$

Parallel lines have equal slopes, so $m = \frac{1}{6}$.

Step2: Use point-slope form

Substitute $(x_1,y_1)=(6,-2)$ and $m=\frac{1}{6}$ into $y - y_1 = m(x - x_1)$:

$$ y - (-2) = \frac{1}{6}(x - 6) $$

Step3: Simplify to slope-intercept form

Simplify the equation:

$$\begin{align*} y + 2 &= \frac{1}{6}x - 1\\ y &= \frac{1}{6}x - 3 \end{align*}$$

Step4: Convert to standard form (optional)

Multiply through by 6 to eliminate fractions:

$$ x - 6y = 18 $$

Answer:

$y = \frac{1}{6}x - 3$ (or $x - 6y = 18$)