# Find the rate of change $dy/dx$ where $x= x_0$

$y= 3x+5$; $x_0=-1$

I know the answer is $3$ but I don't know how to solve it. Can you please help me?

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$\frac{dy}{dx}=3$, a constant. So its value does not depend on $x_0$. – André Nicolas Feb 28 '13 at 23:47
So, that's it? Thank you so much! – Joanna Feb 28 '13 at 23:52
You are welcome. Sometimes when a problem is too simple, it can be puzzling. You might have had an easier time with $y=x^3+5x$. – André Nicolas Feb 28 '13 at 23:59

$${dy \over dx} \equiv \lim_{h \to 0} {f(x+h)-f(x) \over h} \\$$
Where $y = f(x)$.
$${dy \over dx} = \lim_{h \to 0} {3 x + 3 h + 5 - 3 x - 5 \over h} = 3$$
@SeanHaugh Are you sure you mean $\equiv$, instead of $=$? – Jeel Shah Feb 28 '13 at 23:59
@gekkostate, I'm not Sean Haugh, but the $\equiv$ sign is also used for definitions or identities. – George V. Williams Mar 1 '13 at 0:07