Question

How do you find the x and y intercept given `y=3x-6`?

Answer 1

Plug in `0` for `y` and `x`, respectively.

Explanation:

To find the x-intercept, that is, where the line touches the x-axis, the y-value is equal to `0`. Therefore, in order to find the x-intercept, plug `0` into `y` in the original equation.

You get: `0=3x-6`
Now, you must solve for `x`.
Add `6` to both sides: `6=3x`
Divide both sides by `3`: `2=x`
Knowing that `x=2`, we know that the x-intercept is `(2,0)`.

We use the same logic to find the y-intercept, at which we know that `x=0`. So, we will plug that into the original equation.

You get: `y=3*0-6`
Multiply: `y=0-6`
Subtract: `y=-6`
Therefore, the y-intercept is `(0,-6)`.

Another way to find the y-intercept is to recognize that `y=3x-6` is in the general form `y=mx+b`, in which `b` is equal to the y-intercept, which, in this case, is `-6`.