Question

the equation of line q is $y = \frac{1}{6}x - 5$. line r, which is parallel to line q, includes the point (6, 2). what is the equation of line r? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. For line $q: y = \frac{1}{6}x - 5$, the slope $m = \frac{1}{6}$.

Step2: Use point-slope form

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

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$y - 2 = \frac{1}{6}x - 1$
$y = \frac{1}{6}x - 1 + 2$
$y = \frac{1}{6}x + 1$

Answer:

$y = \frac{1}{6}x + 1$