# How do you graph using slope and intercept of 2x - 3y = -11?

May 18, 2016

#### Explanation:

To graph $2 x - 3 y = - 11$, we have to convert this into slope intercept form.

Slope intercept form of the equation is $y = m x + c$, where $m$ is slope and $c$ is the intercept made by line on $y$ axis.

As $2 x - 3 y = - 11$, we have $3 y = 2 x + 11$ or $y = \frac{2}{3} x + \frac{11}{3}$

Hence slope of $2 x - 3 y = - 11$ is $\frac{2}{3}$ and intercept made by line on $y$ axis is $\frac{11}{3}$.

So first mark the point $\left(0 , \frac{11}{3}\right)$ and then one needs to draw a line with slope $\frac{2}{3}$ from this point. As it is upward sloping, one needs to add $2$ units on ordinate and $3$ units on abscissa.

So other point could be $\left(3 , 2 + \frac{11}{3}\right)$ or $\left(3 , 5 \frac{2}{3}\right)$ and the line should look like

graph{2x-3y=-11 [-20, 20, -10, 10]}