How do you calculate slope from a graph?

1 Answer
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:

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

Therefore,
Slope of the given line = tanthetatanθ

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^o30o,

Slope of the given line = tan30=1/sqrt3tan30=13

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=0Ax2+By+C=0

where A,B and CA,BandC are some constants.

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

Then, the slope of the line = -A/BAB

For example, let the equation of the given line be x^2+3=2yx2+3=2y.

Rewriting in the standard form, we get: x^2-2y+3=0x22y+3=0
and we can see that:
A=1A=1
B=-2B=2
C=3C=3

Therefore, the slope of the line =-A/B=-(1)/(-2)=1/2=AB=12=12