Question

what is an equation of the line that passes through the point (-5,5) and is parallel to the line $x + 5y = 25$?

Explanation:

Step1: Find the slope of the given line

Rewrite $x + 5y=25$ in slope - intercept form $y=mx + b$ (where $m$ is the slope).
$5y=-x + 25$, so $y=-\frac{1}{5}x+5$. The slope $m =-\frac{1}{5}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-5,5)$ and $m =-\frac{1}{5}$.
$y - 5=-\frac{1}{5}(x + 5)$.

Step3: Simplify the equation

$y-5=-\frac{1}{5}x - 1$.
$y=-\frac{1}{5}x+4$.

Answer:

$y =-\frac{1}{5}x + 4$