Determining the Equation of a Line

Now that you can find the slope of a line, it is time to determine the equation of a given line. The general formula for the equation of a line is:

y = mx + b
where:
m = the slope of the line
b = the point at which the line crosses the vertical (or y) axis. (Also known as the y-intercept).

You can see how this works in the example below:

Example

Find the equation of the line below:

Solution

In order to find the equation of this line, we need to find the slope and the y - intercept. The value of the y-intercept is easy to find as it requires no calculation. The value where the graph crosses the vertical axis is 150. Therefore b = 150.

Now we have to find the value of the slope. Two points have been shown on the graph for your convenience. In this example, the rise is 150 (350 - 200) and the run is 60 (80 - 20). Therefore, using slope = rise/run, we see that the slope is:

slope = rise/run
slope = 150/60
slope = 2.5

So now we know that the value of m is 2.5, and the value of b is 150. Plug these into the general equation to get:

y = 2.5x + 150

This is the equation of the line shown above.

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