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

1 Answer
Lovecraft
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(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.

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