# How do you rewrite the equation 2y+3x=4 in slope intercept form?

Jun 19, 2018

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

#### Explanation:

First, write the equation

$y = m x + b$

and look at the equation you are given. From there, solve the equation to get $y$ by itself you will end up with

$2 y = 4 - 3 x$

Then, divide both sides by two to get the unit rate

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

After, switch the two values on the right side to get

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

I hope this helps!

Jun 19, 2018

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

#### Explanation:

Given:

$2 y + 3 x = 4$

Rewrite in the standard form for a linear equation: $A x + B y = C$

$3 x + 2 y = 4$

The slope-intercept form for a linear equation is $y = m x + b$,

where:

$m$ is the slope and $b$ is the y-intercept.

To convert the standard form to slope-intercept form, solve for $y$.

$3 x + 2 y = 4$

Subtract $3 x$ from both sides.

$2 y = - 3 x + 4$

Divide both sides by $2$.

$y = - \frac{3}{2} x + \frac{4}{2}$

Simplify.

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

graph{(3x+2y-4)(y+3/2x-2)=0 [-9.96, 10.04, -2.76, 7.24]}