Question

what is an equation of the line that passes through the point (-5, -7) and is parallel to the line 3x - 5y = 10?

Explanation:

Step1: Find the slope of the given line

Rewrite $3x - 5y=10$ in slope - intercept form $y = mx + b$ (where $m$ is the slope).
$-5y=-3x + 10$, so $y=\frac{3}{5}x-2$. The slope $m=\frac{3}{5}$. Parallel lines have the same slope.

Step2: Use the point - slope form to find the equation of the new line

The point - slope form is $y - y_1=m(x - x_1)$, with $(x_1,y_1)=(-5,-7)$ and $m = \frac{3}{5}$.
$y-(-7)=\frac{3}{5}(x - (-5))$.

Step3: Simplify the equation

$y + 7=\frac{3}{5}(x + 5)$
$y+7=\frac{3}{5}x+3$
$y=\frac{3}{5}x-4$

Answer:

$y=\frac{3}{5}x - 4$