# Need help with this linear equation

Trying to figure out what went wrong with the way I solved this

So, a linear function is given. It's $g(x) = 10x + 5$

I know that $\frac{g(a+h) - g(a)}{(a+h) - a}$

I came up with $\frac{[10(a+h) +2] - [10a + 5]}{h}$

I then simplified that down and came up with 20, but apparently that's wrong?

What did I do wrong?

Edit: Ah, I forgot to say I'm trying to find the average rate of change of the function between $x = a$ and $x = a + h$.

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It is not clear at all what you are asking. Your title says linear equations, but you seem to be talking about some kind of difference quotient? Also, if this is homework, please indicate it in the tags. – Daniel Littlewood Sep 23 '12 at 19:18

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Yes, it's wrong. $$\dfrac{(10 (a+h) + 5) - (10 a + 5)}{h} = 10$$ – Robert Israel Sep 23 '12 at 19:19
Note $g(a+h)=10(a+h)+5$, not $10(a+h)+2$ as you have. Still, with what you have, your simplification went awry. You should not have obtained "$20$". Try going through it again (with the proper value of $g(a+h)$, of course)... – David Mitra Sep 23 '12 at 19:23

## 1 Answer

$\frac{g(a+h)-g(a)}{(a+h)-a}=\frac{10a+10h+5-10a-5}{h}=\frac{10h}{h}=10$ shows that any difference quotient is $10$.

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Figured what I did wrong; didn't distribute a minus sign. Simple error, thanks guy! – Brandt Sep 23 '12 at 19:26
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