# What is the slope and x and y intercepts of x=-4y-12?

##### 1 Answer
May 15, 2018

Slope: $- \frac{1}{4}$

$x$-axis intercept: $\left(- 12 , 0\right)$

$y$-axis intercept: $\left(0 , - 3\right)$

#### Explanation:

To find the intercepts, set one variable as zero and solve for the other:

$x$ intercept:

set $y = 0$ and find $x$:

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

So, the $x$-axis intercept is the points $\left(- 12 , 0\right)$

$y$ intercept:

set $x = 0$ and find $y$:

$0 = - 4 y - 12 \setminus \iff 4 y = - 12 \setminus \iff y = - 3$

So, the $y$-axis intercept is the points $\left(0 , - 3\right)$

Slope

transform the equation in the slope-intercept form $y = m x + q$:

$x = - 4 y - 12 \setminus \iff 4 y = - x - 12 \setminus \iff y = - \frac{1}{4} x - 3$

so, the slope is $m = - \frac{1}{4}$

Here you can check the intercepts, and that the slope is indeed negative:
graph{-x/4-3 [-14.676, 1.904, -5.38, 2.91]}