Question

An equation for the line through (-7, -8) that is parallel to y=-3/5x -7

Answer 1

Given:

The line passes through the point is (-7, -8) and parallel to the line

$y=-\frac{3}{5}x-7$

To find:

The equation of the line.

Explanation:

Since the lines are parallel. So, the slope of the line is

$m=-\frac{3}{5}$

Using the point-slope formula,

$\begin{gathered} (y-y_1)=m(x-x_1) \\ y-(-8)=-\frac{3}{5}(x-(-7)) \\ y+8=-\frac{3}{5}(x+7) \\ y+8=-\frac{3}{5}x-\frac{21}{5} \\ y=-\frac{3}{5}x-\frac{21}{5}-8 \\ y=-\frac{3}{5}x-\frac{21}{5}-\frac{40}{5} \\ y=-\frac{3}{5}x-\frac{61}{5} \end{gathered}$

Hence, the equation of the line is,

$y=-\frac{3}{5}x-\frac{61}{5}$

Final answer:

The equation of the line is,

$y=-\frac{3}{5}x-\frac{61}{5}$