Question

Which are the intercepts of the equation y+2=4(x+1) ?

Answer 1

x-intercept is (
`- (1)/(2), 0`) and y-intercept is (
`0, 2`)

Explanation:

How do we find the y-intercept of a function?

We solve the equation when x=0. Let's try that with
`y+2=4(x+1)`

First, let's simplify it so that it resembles
`y=mx+b` more noticeably

`y = 4x + 4 - 2 \\y = 4x + 2`

Now let's plug in 0 for x to find the y-intercept:

`y = 4\cdot 0 + 2\\y = 2`

How do we find the x-intercept of a function?

We solve the equation when y=0. Let's try this from the simplified equation we got (
`y = 4x + 2`)

`0 = 4x + 2\\-2 = 4x\\(-2)/(4) = x\\x = - (1)/(2)`

We must remind ourselves that all y-intercepts have an x that is equal to 0 and that all x-intercepts have a y equal to 0.

That means that our x-intercept will be (
`- (1)/(2), 0`) and our y-intercept will be (
`0, 2`)

This corresponds to the 3rd option counting from the left.

Good luck!