# How do you write an equation that contains points (-1, 2) and is parallel to x-2y=-3?

Sep 24, 2015

$1 x - 2 y = - 6$

#### Explanation:

All lines parallel to $x - 2 y = - 3$ will have the same slope as $x - 2 y = - 3$

That is all lines parallel to $x - 2 y = - 3$ will have a slope $m = \frac{1}{2}$ (see below if the reason for this isn't obvious)

Using the slope point form (with point $\left(\hat{x} , \hat{y}\right) = \left(- 1 , 2\right)$ and slope $m = \frac{1}{2}$)
we have
$\textcolor{w h i t e}{\text{XXXX}} \left(y - 2\right) = \frac{1}{2} \left(x - \left(- 2\right)\right)$
which we could simplify as
$\textcolor{w h i t e}{\text{XXXX}} 2 y - 4 = x + 2$
or in standard form as
$\textcolor{w h i t e}{\text{XXXX}} 1 x - 2 y = - 6$

further explanation
How do we know the slope of $x - 2 y = - 3$ has a slope of $\frac{1}{2}$?

We can rearrange $x - 2 y = - 3$ as
$\textcolor{w h i t e}{\text{XXXX}} - 2 y = - x - 3$
or
$\textcolor{w h i t e}{\text{XXXX}} y = \frac{1}{2} x + \frac{3}{2}$
which is ane equation in slope-intercept form
with a slope of $\frac{1}{2}$
(and a y-intercept of $\frac{3}{2}$, although this isn't relevant to this question)