Question

How do you find the x and y intercepts of `y=2/3x-4`?

Answer 1

See the entire solution process below:

Explanation:

To find the y-intercept by substitution, substitute `0` for `x` and calculate `y`:

`y = (2/3 xx 0) - 4`

`y = 0 - 4`

`y = -4` Therefore the y-intercept is `-4` or `(0, -4)`

To find the x-intercept by substitution, substitute `0` for `y` and solve for `x`:

`0 = 2/3x - 4`

`0 + color(red)(4) = 2/3x - 4 + color(red)(4)`

`4 = 2/3x - 0`

`4 = 2/3x`

`color(red)(3)/color(blue)(2) xx 4 = color(red)(3)/color(blue)(2) xx 2/3x`

`12/color(blue)(2) = cancel(color(red)(3))/cancel(color(blue)(2)) xx color(blue)(cancel(color(black)(2)))/color(red)(cancel(color(black)(3)))x`

`6 = x`

`x = 6` Therefore the x-intercept is `6` or `(6, 0)`