Let $f$ be a linear function for which $f(6)-f(2)=12$. What is $f(12)-f(2)?$ Please explain how you found your answer. Thank you!

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Explanation:

Since f(x) is linear, this means f(x) = mx+b

Let's plug in x = 6

Repeat for x = 2

Now subtract the two function outputs

The b terms cancel out which is very handy.

Set this equal to 12, since f(6)-f(2) = 12, and solve for m

So the slope of f(x) is m = 3

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Next, plug in x = 12

We can then say:

Lastly, we plug in m = 3