# How do you find the instantaneous rate of change of y=5x+9 at x=2?

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Feb 17, 2017

5

#### Explanation:

$y = 5 x + 9$ is a line in the form of $y = m x + b$

This means that the slope $m$ at any point will the the same value, in this case, $5$. (Lines have constants slopes or rates of change.)

Using derivatives, we find that the $y ' = 5$ which confirms that the slope is $5$ regardless of what the $x$ value is. We only need to find the slope at a specific $x$ value if the derivative has an $x$ term in it.

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