# How do you graph 2x - 3y = 9 using x- and y- intercepts?

Mar 19, 2018

See a solution process below:

#### Explanation:

First, find the y-intercept: Set $x = 0$ and solve for $y$:

$\left(2 \cdot 0\right) - 3 y = 9$

$0 - 3 y = 9$

$- 3 y = 9$

$\frac{- 3 y}{\textcolor{red}{- 3}} = \frac{9}{\textcolor{red}{- 3}}$

$y = - 3$ or $\left(0 , - 3\right)$

Next, find the x-intercept: Set $y = 0$ and solve for $x$:

$2 x - \left(3 \cdot 0\right) = 9$

$2 x - 0 = 9$

$2 x = 9$

$\frac{2 x}{\textcolor{red}{2}} = \frac{9}{\textcolor{red}{2}}$

$x = \frac{9}{2}$ or $\left(\frac{9}{2} , 0\right)$

We can next plot the two points on the coordinate plane:

graph{(x^2+(y+3)^2-0.075)((x-(9/2))^2+y^2-0.075)=0 [-20, 20, -10, 10]}

Now, we can draw a straight line through the two points to graph the line:

graph{(2x - 3y - 9)(x^2+(y+3)^2-0.075)((x-(9/2))^2+y^2-0.075)=0 [-20, 20, -10, 10]}