# How do you find an equation of a line containing the point (-2, 2), and parallel to the line 2(y + 1) = x?

Jul 17, 2017

$y = \frac{1}{2} x + 3$

#### Explanation:

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.

$2 \left(y + 1\right) = x \text{ } \rightarrow y + 1 = \frac{1}{2} x$

Then: $y = \frac{1}{2} x - 1 \text{ } \leftarrow$ this gives the slope as $m = \frac{1}{2}$

Now use the point slope formula for a line:

$y - {y}_{1} = m \left(x - {x}_{1}\right) \text{ }$with $\left(- 2 , 2\right) \mathmr{and} m = \frac{1}{2}$

$y - 2 = \frac{1}{2} \left(x - \left(- 2\right)\right)$

$y = \frac{1}{2} x + 1 + 2$

$y = \frac{1}{2} x + 3$