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

Mar 20, 2018

$m = \frac{2}{5}$

#### Explanation:

Given the equation of a line, all we need to do is rearrange it into terms of $y = m x + b$

$5 y - 2 x = - 3$
$5 y = 2 x - 3$ Add -2x to both sides to get $y$ by itself
$y = \frac{2}{5} x - \frac{3}{5}$ Divide all terms by 5

Now that the equation is in terms of slope-intercept, with the slope being $m$ in $y = m x + b$, you can find the slope.

Mar 20, 2018

See a solution process below:

#### Explanation:

We can multiply each side of the equation by $\textcolor{red}{- 1}$ to put the equation in Standard Linear Form. The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

$\textcolor{red}{- 1} \left(5 y - 2 x\right) = \textcolor{red}{- 1} \cdot - 3$

$\left(\textcolor{red}{- 1} \times 5 y\right) - \left(\textcolor{red}{- 1} \times 2 x\right) = 3$

$- 5 y - \left(- 2 x\right) = 3$

$- 5 y + 2 x = 3$

$\textcolor{red}{2} x + \textcolor{b l u e}{- 5} y = \textcolor{g r e e n}{3}$

The slope of an equation in standard form is: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

Substituting gives:

$m = \frac{- \textcolor{red}{2}}{\textcolor{b l u e}{- 5}} = \frac{2}{5}$

Mar 20, 2018

slope=$\frac{2}{5}$

#### Explanation:

So you're going to want to get it into $m x + b = y$ form, where $m$ is the slope and $b$ is the $x$ intercept.

To rearrange the equation:
$5 y - 2 x = - 3$
add $2 x$ to each side, which cancels out $- 2 x$ from the left side
$5 y = - 3 + 2 x$
now divide each side by $5$, which crosses out the $5$ in $5 y$
$y = \frac{- 3 + 2 x}{5}$

You now have the correct arrangement of the equation and can even flip $- 3$ and $2 x$ to match the form of the equation you want it in

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

Now since you have the equation being divided by $5$, you have to divide both $2$ and $3$ by $5$, making your new equation:
$y = \left(\frac{2}{5}\right) x - \left(\frac{3}{5}\right)$

and following the equation we can now see that $m$, which is the slope, is equal to $\frac{2}{5}$.