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Question 506437: I'm not sure how to determine whether or not a function is linear. I know and understand what a linear function is, but I'm not sure how to immediately determine it. I know it has something to do with f(x)= mx+b. My teacher taught me something about A, B, and C. I'm not sure what he exactly means by this. The problems I'm having trouble are:
1. x/2=10+2y/3
2. 3a+b-2=b
3. 3m/4= 2n/3-5
Is there anyway where I can immediately identify it as linear or non-linear without graphing it or testing the function out?
Answer by Sarah900(12)   (Show Source):
You can put this solution on YOUR website! A linear equation can be written in the Standard form which is Ax+By=C The important thing here is that neither x, nor y is in a denominator, radical, or exponent. They are not multiplied together and they are being taken to an exponent of 1. For example the first equation can be rewritten as
x/2-2y/3=10
In this case 1/2=A -2/3=B and 10=C
In the second one the b's cancel leaving
3a=2
This is also in standard form. The B in this case just happens to be 0.
If you rearrange the last problem you will find it can also be placed in Standard form.
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