# How do you graph 2x-3y=6 using slope intercept form?

Dec 23, 2014

You can first re-arrange your expression by letting $y$ alone on one side:
$2 x - 3 y = 6$
$- 3 y = 6 - 2 x$
and finally:
$y = \frac{2}{3} x - 2$

$\frac{2}{3}$ is the SLOPE. It tells you how the value of $y$ changes when $x$ changes. In this case for each change of 1 in $x$ you have a change of $\frac{2}{3}$ in $y$.
$- 2$ is the intercept on the $y$ axis.

You now have the coordinates of:
1) intercept y axis: $\left(0 , - 2\right)$
2) intercept x axis: $\left(3 , 0\right)$