Question

How do you find the y intercept for 8x + 4y = 24?

Answer 1

`b = 6`

Explanation:

The y intercept is the value of the function when the curve intercepts the y-axis, or, in other terms, `f(0)`.

While we're more used to dealing with lines in the form of `y = ax + b` it's the same concept with lines in that form.

Substitute `x` for `0`
`8x + 4y = 24`
`8*0 +4y = 24`
`4y = 24`

Isolate `y`
`y = 24/4 = 6`

And there you go, the y intercept is `6`.

Or, you can put in an easy to recognize way we're more used to, isolate y without substituting the x, to make the function more traditional, i.e.: in the form of `y = ax+b`
`8x + 4y = 24`
`4y = 24 - 8x`
`y = (24 - 8x)/4`
`y = (4*(6-2x))/4`
`y = 6 - 2x rarr y = -2x + 6`

We know `a` is the slope and `b` is the y-intercept without even having to substitute. But it's good to know both ways because sometimes it's just easier to do it the other way. Like it was this time.