# Find an equation of a line containing the point (-2, 2), and parallel to the line 2(y + 1) = x

Find an equation of a line containing the point (-2, 2), and parallel to the line 2(y + 1) = x
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encaselatqr
We are given a point on the line and have indirectly been given the slope as well, because lines that are parallel have the same slope.
Simplify the equation of the given line.
$2\left(y+1\right)=x\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}\to y+1=\frac{1}{2}x$
Then: $y=\frac{1}{2}x-1\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}←$ this gives the slope as $m=\frac{1}{2}$
Now use the point slope formula for a line:
$y-{y}_{1}=m\left(x-{x}_{1}\right)\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}$ with $\left(-2,2\right)\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}m=\frac{1}{2}$
$y-2=\frac{1}{2}\left(x-\left(-2\right)\right)$
$y=\frac{1}{2}x+1+2$
$y=\frac{1}{2}x+3$