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

Sep 18, 2015

$b = 6$

#### Explanation:

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

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

Substitute $x$ for $0$
$8 x + 4 y = 24$
$8 \cdot 0 + 4 y = 24$
$4 y = 24$

Isolate $y$
$y = \frac{24}{4} = 6$

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 $y = a x + b$
$8 x + 4 y = 24$
$4 y = 24 - 8 x$
$y = \frac{24 - 8 x}{4}$
$y = \frac{4 \cdot \left(6 - 2 x\right)}{4}$
$y = 6 - 2 x \rightarrow y = - 2 x + 6$

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.