# Derivative of Linear Function

In this tutorial we discuss the derivative of linear function or derivative of straight line equation in the form of slope intercept.
Let us suppose that linear function of the form $y = mx + c$ where $m$ is slope and $c$ is Y-intercept represents the equation of straight line.

Differentiating the given linear function with respect to $x$, we get

In the given function we have two values, now differentiate separately we get

Using the following formulae $\frac{d}{{dx}}\left( x \right) = 1$ and $\frac{d}{{dx}}\left( c \right) = 0$to evaluate given function as

We concluded that the derivative of given function is the slope of function.

Example: Find the derivative of $y = f\left( x \right) = 9x + 10$
We have the given function as

Differentiation with respect to variable $x$, we get

Now using the formulas $\frac{d}{{dx}}\left( x \right) = 1$and $\frac{d}{{dx}}\left( c \right) = 0$, we have