Question

question
find the equation of a line parallel to $-5x + y = 5$ that passes through the point $(8, 6)$.

answer
$y + 6 = 5(x - 8)$
$y - 6 = 5(x + 8)$
$y - 6 = -\frac{1}{5}(x - 8)$
$y - 6 = 5(x - 8)$

Explanation:

Step1: Find slope of given line

Rewrite $-5x + y = 5$ to slope-intercept form $y=mx+b$:
$y = 5x + 5$
Slope $m = 5$

Step2: Use point-slope form

Parallel lines have equal slopes. Use point $(8,6)$ and $m=5$ in $y-y_1=m(x-x_1)$:
$y - 6 = 5(x - 8)$

Answer:

$y - 6 = 5(x - 8)$