Question

How do you find the x and y intercepts for `y=3x-2`?

Answer 1

`y = -2`
`x = 0`
`(0,-2)`

Explanation:

Add two to both sides.
`y = 3x - 2`
to
`y + 2 = 3x`

Next, instead of `x`, put `y + 2`.
`y + 2= 3(y+2)`

Then, multiply `3` by `y` and `3` by `2`.
`y +2= 3y + 6`

Subtract `y` from both sides.
`2 + y = 3y + 6`
to
`2 = 2y + 6`

Subtract `6` from both sides.
`2 = 2y + 6`
to
`-4 = 2y`

Divide both sides by `2`.
`-4 = 2y`
to
`-2 = y`
Go back to the original equation. Replace `y` with `-2`.
`y = 3x - 2`
to
`-2 = 3x - 2`

Add `2` to both sides.
`-2 = 3x - 2`
to
`0 = 3x`

Divide both sides by `3`.
`0 = 3x`
to
`0 = x`

Hope that helped! : )

Answer 2

The x-intercept is `(2/3,0)`.

The y-intercept is `(0,-2)`.

Explanation:

Given:

`y=3x-2`

X-intercept: value of `x` when `y=0`.

Substitute `0` for `y`.

`0=3x-2`

Add `2` to both sides.

`2=3x`

Divide both sides by `3`.

`2/3=x`

The x-intercept is `(2/3,0)`.

Y-intercept: value of `y` when `x=0`

`y=3x-2` is the slope-intercept form for a linear equation:

`y=mx+b`,

where:

`m` is the slope, and `b` is the y-intercept.

Therefore, the y-intercept is `(0,-2)`.

You can also substitute `2` for `x` and solve for `y`.

`y=3(0)-2`

`y=-2`

The y-intercept is `(0,-2)`.

graph{y=3x-2 [-10, 10, -5, 5]}