Question

How do you find the slope and intercept of `y = 4/3x - 3`?

Answer 1

The slope is `4/3`.

The `x`-intercept is at `(9/4, 0)`.

The `y`-intercept is at `(0, -3)`.

Explanation:

`y = 4/3x - 3`

This equation is in slope-intercept form:

We know the slope is the value multiplied by `x`, so the slope is `4/3`.

To find the `x-`intercept, plug in `0` for `y` and solve for `x`:
`0 = 4/3x - 3`

Add `color(blue)3` to both sides:
`0 quadcolor(blue)(+quad3) = 4/3x - 3 quadcolor(blue)(+quad3)`

`3 = 4/3x`

Multiply both sides by `color(blue)(3/4)`:
`3 color(blue)(*3/4) = 4/3x color(blue(*3/4)`

`9/4 = x`

`x = 9/4`

Therefore, the `x`-intercept is at `(9/4, 0)`.

To find the `y`-intercept, plug in `0` for `x` and solve for `y`:
`y = 4/3(0) - 3`

`y = 0 - 3`

`y = -3`

Therefore, the `y`-intercept is at `(0, -3)`.

Hope this helps!

Answer 2

Slope `4/3`, `x`-int `9/4`, `y`-int `-3`

Explanation:

This equation is in slope-intercept form

`y=mx+b`, with slope `m` and a `y`-intercept of `b`. By pattern matching, we see our slope is `4/3` and our `y`-intercept is `-3`.

We can find the `x`-intercept by setting `y` equal to zero. We get

`0=4/3x-3=4/3x=3=>x=9/4`

Therefore, our slope is `4/3`, our `y`-intercept is `-3`, and our `x`-intercept is `9/4`.

Hope this helps!