Question

How do you find the `x` and `y`-intercept for the equation: 4x - 3y - 6 = 0#?

Answer 1

See a solution process below:

Explanation:

x-intercept: Set `y` to `0` and solve for `x`:

`4x - 3y - 6 = 0` becomes:

`4x - (3 * 0) - 6 = 0`

`4x - 0 - 6 = 0`

`4x - 6 = 0`

`4x - 6 + color(red)(6) = 0 + color(red)(6)`

`4x - 0 = 6`

`4x = 6`

`(4x)/color(red)(4) = 6/color(red)(4)`

`(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 6/4`

`x = 3/2`

The x-intercept is: `x = 3/2` or `(3/2, 0)`

y-intercept: Set `x` to `0` and solve for `y`:

`4x - 3y - 6 = 0` becomes:

`(4 * 0) - 3y - 6 = 0`

`0 - 3y - 6 = 0`

`-3y - 6 = 0`

`-3y - 6 + color(red)(6) = 0 + color(red)(6)`

`-3y - 0 = 6`

`-3y = 6`

`(-3y)/color(red)(-3) = 6/color(red)(-3)`

`(color(red)(cancel(color(black)(-3)))y)/cancel(color(red)(-3)) = 6/-3`

`y = -2`

The y-intercept is: `y = -2` or `(0, -2)`