Question

What is the `y`-intercept of the line `3x-4y=24`?

Answer 1

See a solution process below:

Explanation:

This equation is in Standard Linear form. The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

Where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

The slope of an equation in standard form is: `m = -color(red)(A)/color(blue)(B)`

The `y`-intercept of an equation in standard form is: `color(green)(C)/color(blue)(B)`

`color(red)(3)x - color(blue)(4)y = color(green)(24)`

Or

`color(red)(3)x + color(blue)(-4)y = color(green)(24)`

Substituting the values from the equation gives the `y`-intercept as:

`color(green)(24)/color(blue)(-4) = -6` or `(0, -6)`

Answer 2

`(0,-6)`

Explanation:

Rearrange

`3x=4y+24`

`3x-24=4y`

`y=3/4x-6`

Answer 3

`(0,-6)`

Explanation:

The `y`-intercept is when `x` is equal to zero, so let's just plug zero into our equation for `x`.

The `x` term will just disappear, and we're left with

`-4y=24=>y=-6`

Dividing both sides by `-4`, we find that the `y`-intercept of the line occurs at `(0,-6)`.

The nice thing about equations of lines in standard form is that it is very easy to find the intercepts.

To find the `y`-intercept, set `x` equal to zero.

To find the `x`-intercept, set `y` equal to zero.

Hope this helps!