Question

How do you calculate slope from a graph?

Answer 1

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`