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

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Answer 1 · 2018-05-15T08:02:07

Slope: $-1/4$

$x$ -axis intercept: $(-12,0)$

$y$ -axis intercept: $(0,-3)$

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

$x$ intercept:

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

$x = -4(0)-12 =-12$

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

$y$ intercept:

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

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

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

Slope

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

$x=-4y-12 \iff 4y=-x-12 \iff y=-1/4x-3$

so, the slope is $m=-1/4$

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]}