# What are three ways to find the slope of a line?

Apr 10, 2015

Three ways to find the slope of a line:

1. You may have two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ (often one or both of these points may be intercepts of the $x$ and/or $y$ axes). The slope is given by the equation
$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

2. You may have a linear equation that is either in the form or can be manipulated into the form
$y = m x + b$.
In this case the slope is $m$ (the coefficient of $x$).

3. If the line is a tangent to another function, you may have (or be able to determine) the slope of the tangent as the derivative of the function. Normally in this case the derivative is a function expressed in terms of $x$ and you need to substitute the value of $x$ into this function for the required location.