# How do you write 3x - 2y= 5  into slope intercept form?

Aug 22, 2015

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

#### Explanation:

For a general line $y$, the equation of the line in slope-intercept form looks like this

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

$m$ - the slope of the line;
$b$ - the $y$-intercept.

So basically, all you have to do to write the equation for your line in sloper-intercept form is isolate $y$ on one side of the equation.

Start by adding $- 3 x$ to both sides to get

$- \textcolor{red}{\cancel{\textcolor{b l a c k}{3 x}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{3 x}}} - 2 y = 5 - 3 x$

$- 2 y = - 3 x + 5$

Now divide both sides of the equation by $- 2$ to get

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} \cdot y}{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}}} = \frac{\left(- 3\right)}{\left(- 2\right)} x + \frac{5}{\left(- 2\right)}$

$\textcolor{g r e e n}{y = \frac{3}{2} x - \frac{5}{2}}$