# How do you find the slope of 5x + 3y = -2?

Jun 25, 2016

slope $= - \frac{5}{3}$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{slope-intercept form}}$ is

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where m represents the slope and b, the y-intercept.

The advantage to having the equation in this form is that m and b can be extracted 'easily'.

Rearrange 5x + 3y = - 2 into this form.

leave 5y on the left and move 5x to the right.

subtract 5x from both sides

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

now divide both sides by 3

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

$\Rightarrow \text{slope} = - \frac{5}{3}$