# What is the slope and intercept for  2x+3y=9 and how would you graph it?

Oct 7, 2015

$m = - \frac{2}{3}$

$c = 9$

#### Explanation:

A straight line graph is of the form:

$y = m x + c$

$m$ is the gradient

$c$ is the intercept which is the point at $x = 0$ where the line cuts the $y$ axis.

So we get our equation into this form:

$2 x + 3 y = 9$

$3 y = - 2 x + 9$

$y = - \frac{2}{3} x + 9$

So the slope or gradient $m = - \frac{2}{3}$

The intercept $c = 9$

To graph it manually just pick a range of values of $x$ and find the corresponding value of $y$.

e.g $x = 1 \Rightarrow$

$y = - \left(\frac{2}{3} \times 1\right) + 9 = = \frac{25}{3}$

So your 1st point is $\left[1 , \frac{25}{3}\right]$

You should end up with this:

graph{-2/3x+9 [-16.5, 23.5, -8.7, 11.3]}