# How do you write an equation in slope intercept form given (-2, 3) and is parallel to 3x + 2y = 10?

May 10, 2016

$y - 3 = - \frac{3}{2} \left(x + 2\right)$

#### Explanation:

Things to Remember

1. A line with the general form: $\textcolor{w h i t e}{\text{XXX}} A x + B y = C$
has a slope of $\textcolor{w h i t e}{\text{XXX}} m = - \frac{A}{B}$

2. All parallel lines have the same slope.

3. The slope-point form for a line with slope $m$ through a point $\left(a , b\right)$ is
$\textcolor{w h i t e}{\text{XXX}} y - b = m \left(x - a\right)$

Therefore for this example

a. $3 x + 2 y = 10$ has a slope of $m = - \frac{3}{2}$

b. All lines parallel to $3 x + 2 y = 10$ have a slope of $m = - \frac{3}{2}$

c. The slope point form for a line with slope $m = - \frac{3}{2}$ through the point $\left(- 2 , 3\right)$ is
$\textcolor{w h i t e}{\text{XXX}} y - 3 = - \frac{3}{2} \left(x + 2\right)$