# How do you write an equation of a line parallel to the graph of 2x+5y=3 and the x-intercept is -2?

Apr 9, 2016

$2 x + 5 y = - 4$

#### Explanation:

Any equation of the form $A x + B y = C$ has a slope of $m = - \frac{A}{B}$

Therefore $2 x + 5 y = 3$ has a slope of$\left(- \frac{2}{5}\right)$

All parallel lines have the same slope.

If a line has an x-intercept of $\left(- 2\right)$
then $\left(x , y\right) = \left(- 2 , 0\right)$ is a point on the line.

Using the slope definition:
$\textcolor{w h i t e}{\text{XXX}} \frac{y - 0}{x - \left(- 2\right)} = \left(- \frac{2}{5}\right)$

$\textcolor{w h i t e}{\text{XXX}} y = \left(- \frac{2}{5}\right) \left(x + 2\right)$

$\textcolor{w h i t e}{\text{XXX}} 5 y = - 2 x - 4$

$\textcolor{w h i t e}{\text{XXX}} 2 x + 5 y = - 4$ (standard linear form)