Question

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

Answer 1

x-intercept`=(-9/4,0)`
y-intercept`=(0,-3/4)`

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`.

`-4x-12y=9`

`-4x-12(0)=9`

`-4x=9`

`color(green)(x=-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`.

`-4x-12y=9`

`-4(0)-12y=9`

`-12y=9`

`y=-9/12`

`color(green)(y=-3/4)`

`:.`, the x-intercept is `(-9/4,0)` and the y-intercept is `(0,-3/4)`.