# How do you write an equation of a line going through (-2,1) parallel to y = 1/2x - 3?

Sep 25, 2016

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

#### Explanation:

If the lines are parallel, then the slopes are the same.

$y = \textcolor{red}{\frac{1}{2}} x - 3$ gives you $\textcolor{red}{m = \frac{1}{2}}$

You also have a point, $\left(- 2 , 1\right) \text{ which is } \left(x , y\right)$

So, you can now substitute $m , x , \mathmr{and} y \text{ into } y = m x + c$
to be able to find $c$

$1 = \left(\frac{1}{2}\right) \left(- 2\right) + c$

$1 = - 1 + c$

$\textcolor{b l u e}{2 = c}$

$y = \textcolor{red}{\frac{1}{2}} x \textcolor{b l u e}{+ 2}$