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

May 6, 2018

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

#### Explanation:

You want to convert the equation to the form: $y = m x + b$, where $m$ is the slope, and $b$ is the y-intercept.

$\left[1\right] \text{ } 3 x + 5 y = - 2$

Our goal will be to isolate $y$. We start by subtracting $3 x$ from both sides.

$\left[2\right] \text{ } 3 x + 5 y - 3 x = - 2 - 3 x$

$\left[3\right] \text{ } 5 y = - 2 - 3 x$

Next, we want to remove the coefficient of $y$, so we multiply $\frac{1}{5}$ to both sides.

$\left[4\right] \text{ } \left(\frac{1}{5}\right) 5 y = \left(\frac{1}{5}\right) \left(- 2 - 3 x\right)$

$\left[5\right] \text{ } y = - \frac{2}{5} - \left(\frac{3}{5}\right) x$

We have met our goal of converting the equation to slope-intercept form. The slope is simply the coefficient of $x$.

$\therefore \text{ } \textcolor{b l u e}{m = - \frac{3}{5}}$