Question

What are the x and y intercepts of the linear equation: `-y=(3x+6)-12`?

Answer 1

y-int = 6
x-int = 2

Explanation:

`-y=(3x+6)-12`

first remove the parentheses:
`-y=3x+6 -12`

combine like terms
`-y=3x-6`

multiply both sides by -1
`(-1)-y=(-1)(3x-6)`

`y=-3x+6`

to find the y-intercept set x = 0

`y=-3(0)+6`

`y=6`

to find the x-intercept set y = 0

`0=-3x+6`

`-6=-3x`

`2 = x` or `x = 2`

graph{y=-3x+6 [-13.71, 14.77, -6.72, 7.52]}

Answer 2

`x-`intercept is `(2,0)`
`y-`intercept is `(0,6)`

Explanation:

`-y =(3x+6)-12`

First let's restate the equation in more common form.

(i) The parentheses are serving on purpose here.

`-y =3x+6-12`

`-y=3x-6`

(ii) Multiply through by `-1`

`y = -3x+6`

Here we have the equation in slope/intercept form: `y=mx+c`

Hence the `y-`intercept is `(0,6)`

The `x-`intercept occurs where `y=0 ->`

`0 = -3x+6`

`3x=6 -> x=2`

`:.` the `x-`intercept is `(2,0)`

These intercepts can be seen on the graph of `y` below.

graph{-y =(3x+6)-12 [-16.03, 16.01, -8, 8.03]}