# How do you calculate slope from a graph?

Nov 28, 2014

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 $\theta$.

Therefore,
Slope of the given line = $\tan \theta$

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 ${30}^{o}$,

Slope of the given line = $\tan 30 = \frac{1}{\sqrt{3}}$

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:

$A {x}^{2} + B y + C = 0$

where $A , B \mathmr{and} C$ are some constants.

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

Then, the slope of the line = $- \frac{A}{B}$

For example, let the equation of the given line be ${x}^{2} + 3 = 2 y$.

Rewriting in the standard form, we get: ${x}^{2} - 2 y + 3 = 0$
and we can see that:
$A = 1$
$B = - 2$
$C = 3$

Therefore, the slope of the line $= - \frac{A}{B} = - \frac{1}{- 2} = \frac{1}{2}$