# What are the intercepts of -4x-12y=9?

Jan 31, 2016

x-intercept$= \left(- \frac{9}{4} , 0\right)$
y-intercept$= \left(0 , - \frac{3}{4}\right)$

#### Explanation:

Finding the x-intercept
To find the x-intercept, substitute $y = 0$ into the equation, since the x-intercept of the linear equation will always have a y-coordinate of $0$.

$- 4 x - 12 y = 9$

$- 4 x - 12 \left(0\right) = 9$

$- 4 x = 9$

$\textcolor{g r e e n}{x = - \frac{9}{4}}$

Finding the y-intercept
To find the y-intercept, substitute $x = 0$ into the equation, since the y-intercept of the linear equation will always have an x-coordinate of $0$.

$- 4 x - 12 y = 9$

$- 4 \left(0\right) - 12 y = 9$

$- 12 y = 9$

$y = - \frac{9}{12}$

$\textcolor{g r e e n}{y = - \frac{3}{4}}$

$\therefore$, the x-intercept is $\left(- \frac{9}{4} , 0\right)$ and the y-intercept is $\left(0 , - \frac{3}{4}\right)$.