# What is the equation of a line that is parallel to the line 2x + 5y = -20 and passes through the point (-5,-3)?

May 6, 2015

Your line must have the same slope of the given line to be parallel.
Your line is: $2 x + 5 y = - 20$
this can be written in a "friendlier" way isolating $y$ on one side:
$y = - \frac{2}{5} x - 4$
This is good because you can immediately "see" the slope $m$ as the coefficient of $x$, i.e., $- \frac{2}{5}$
Now you can find the equation of the parallel line using:
$y - {y}_{0} = m \left(x - {x}_{0}\right)$
Try by yourself and if you have problems have a look at the solution below:

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Solution:
using the coordinates of your point and the given slope $m$ you get:
$y - \left(- 3\right) = - \frac{2}{5} \left(x - \left(- 5\right)\right)$
$y + 3 = - \frac{2}{5} x - 2$
$y = - \frac{2}{5} x - 5$