Answer
There are two $x$-intercepts: $2$ and $-2$.
The y-intercept is $9$.
See the graph below.
Work Step by Step
In order to find the $x$-intercept, we have to plug $y=0$ into the equation, and the $x$-coordinate will give us the intercept itself.
$9x^2+4y=36$
$9x^2+4(0)=36$
$9x^2=36$
$x^2=4$
$x=\pm2$
The same thing should be done for the $y$-intercept, however, here $x=0$ should be plugged into the equation.
$9x^2+4y=36$
$9(0)^2+4y=36$
$4y=36$
$y=9$
There are two $x$-intercepts: $2$ and $-2$.
The $y$-intercept is $9$.
Few other points that will help us plot the graph:
If $x=-1$
$9(-1)^2+4y=36$
$4y=27$
$y=\frac{27}{4}=6.75$
The point $(-1,6.75)$ is on the graph.
If $x=1$
$9(1)^2+4y=36$
$4y=27$
$y=\frac{27}{4}=6.75$
The point $(1,6.75)$ is on the graph.
