# How do you find the slope of the graph of 3x+5y=10?

May 5, 2018

$- \frac{3}{5}$ is the slope of the line.

#### Explanation:

Rearrange the equation into slope-intercept form to find the slope:

$y = m x + b$

$\text{m = slope}$
$\text{b = y-intercept}$

So rearrange the problem so that the $y$ is by itself on the left of the equal sign:

$3 x + 5 y = 10$

$5 y = - 3 x + 10$

$y = - \frac{3}{5} x + \frac{10}{5}$

$y = - \frac{3}{5} x + 2$

The slope is next to the $x$, so it is called $m$ in the slope-intercept form:

$y = \textcolor{b l u e}{m} x + b$

$y = \textcolor{b l u e}{- \frac{3}{5}} x + 2$

$- \frac{3}{5}$ is the slope of the line.