Question

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

Answer 1

Slope: `-1/4`

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

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

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(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]}