How do you calculate slope from a graph?

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 = #tantheta#

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 = #tan30=1/sqrt3#

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:

#Ax^2+By+C=0#

where #A,B and C# are some constants.

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

Then, the slope of the line = #-A/B#

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

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

Therefore, the slope of the line #=-A/B=-(1)/(-2)=1/2#