Question

How do you find the intercepts for `y = x - 6`?

Answer 1

The x-intercept is 6
The y-intercept is -6

Explanation:

The x-intercept is the value of `x` at the point where the line of the equation crosses the x-axis. Another way of saying this is that it is the value of `x` when `y=0` (since `y=0` is the equation of the x-axis).
For the equation:
`color(white)("XXXX")` `y=x-6`
setting `y=0`
gives
`color(white)("XXXX")` `0=x-6`
or
`color(white)("XXXX")` `x=6`

Similarly the y-intercept is the value of `y` from the equation when `x=0`
`color(white)("XXXX")` `y=x-6`
becomes
`color(white)("XXXX")` `y=0-6`
or
`color(white)("XXXX")` `y=-6`