Chapter 1.2, Problem 27AYU

In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.

$9x^2+4y=36$

To determine

To find: The intercepts and graph of the equation $9x^2 + \mathrm{4y} = 36$.

Answer to Problem 27AYU

$x\text{-intercept }=\pm 2, y\text{-intercept }=9$

Explanation of Solution

Given:

The equation $9x^2 + \mathrm{4y} = 36$

Calculation:

To find the $x\text{-intercept}$, let $y=0$ implies $9x^2 + 4(0) =\mathrm{ 36}$

$9x^2 = 36$

$x^2=\frac{36}{9}$

$x^2=4$

$x=\pm 2$

$x\text{-intercept}$ is $\pm 2$

To find the $y\text{-intercept}$, let $x=0$ implies $9{(0)}^2+\mathrm{4y}=36$

$\mathrm{4y}=36$

$y=\frac{36}{4}$

$y=9$

$y\text{-intercept}$ is$9$