Question

How do you find the intercepts for `-3x-4y=18`?

Answer 1

`x=-6`

`y=-9/2`

Explanation:

To find the `x` and `y` intercepts for an equation, you need to put the equation in Standard Form (`y=mx+b`).

Thus, we need to solve `-3x -4y = 18` for `y`.

First, we can add `3x` to both sides. Doing so yields:

=`-4y=18+3x`

or

=`-4y=3x+18`

Then, we need to divide both sides by `-4` to isolate `y`.

`y=(3x+18)/(-4)`

Simplifying slightly gets you:

`y=-(3x)/4-18/4`

which equates to

`y=-(3x)/4-9/2`

Now that we have the equation in Standard form, we can look for the intercepts. Conceptually, an `x`-intercept will occur when `y=0` and a `y`-intercept will occur when `x=0`.

So, simply plug in those values of `0` seperately to solve for each intercept.

Solving for the `x`-intercept:

`(0)=-(3x)/4-9/2`

Adding `(3x)/4` to both sides results in:

`(3x)/4=-9/2`

Multiplying both sides by `4/3` gets:

`x=(-9/2)(4/3)`

or:

`x=-6`

Solving for the `y`-intercept:

`y=-(3(0))/4-9/2`

Canceling out the term with the `0` being multiplied to it gives:

`y=-9/2`

It is worthy to notice that the y-intercept of the equation, when put in Standard Form, is simply the term without the `x` in it (or the `b` term when written as `y=mx+b`).