# How do you calculate slope from a graph?

##### 1 Answer

Nuzhat has already discussed how you can find the slope of a line from two points that lie on the line. I'll discuss two other methods of finding the slope from a graph.

**1. From the angle made with the x-axis**

Since the slope of a line is basically *the ratio of the y-component of the line to its x-component*,

The slope of a line can be found out by taking tangent of the angle between the given line and the x-axis.

Consider the following figure:

In this case, the angle between the x-axis and the line is

Therefore,

Slope of the given line =

*Note: Angles in the counterclockwise direction are taken as positive, and those in the clockwise direction are taken as negative.*

For example, if the angle between the x-axis and the given line is

Slope of the given line =

**2. From the equation of the line**

The slope of a line can also be determined from its equation. The standard form of the equation of a line is:

where

First, the equation of the line must be written in the standard form.

Then, the slope of the line =

For example, let the equation of the given line be

Rewriting in the standard form, we get:

and we can see that:

Therefore, the slope of the line