Question

How do you find the `x`-intercept and the `y`-intercept of `5x+4y=-6`?

Answer 1

See a solution process below:

Explanation:

`x`-intercept

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

`5x + 4y = -6` becomes:

`5x + (4 * 0) = -6`

`5x + 0 = -6`

`5x = -6`

`(5x)/color(red)(5) = -6/color(red)(5)`

`(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -6/5`

`x = -6/5`

The `x`-intercept is: `-6/5` or `(-6/5, 0)`

`y`-intercept

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

`5x + 4y = -6` becomes:

`(5 * 0) + 4y = -6`

`0 + 4y = -6`

`4y = -6`

`(4y)/color(red)(4) = -6/color(red)(4)`

`(color(red)(cancel(color(black)(4)))y)/cancel(color(red)(4)) = -(2 xx 3)/color(red)(2 xx 2)`

`y = -(color(red)(cancel(color(black)(2))) xx 3)/color(red)(color(black)(cancel(color(red)(2))) xx 2)`

`y = -3/2`

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