In this video, we are going to look at how to find the equation of a line when given two points.
The equation of a line is written in the form , where is the slope, and is the y-intercept. When given the points (2,3) and (4,7), let’s see how to find the equation of the line. First, let’s find the slope. The equation for the slope is:
Now that we have the slope, let’s see how it looks in the equation of a line.
We still don’t know what is. We do know that the line passes through the two given points. If we pick any one of the two points and plug in their x and y values, then we can solve for . Let’s pick the first point (2,3), and see what we get for .
Now we know that is -1 and is 2. If we go back to our equation of a line and plug these in, then we have:
There is also another way to solve for this as well. The first step is still to find the slope. We already found that the slope is 2 in the last method of solving, so we can just bypass that step. In order to use this other method, we have to use a different form of the equation of a line, called the point-slope form. This is:
In this form, and refer to a point, and is still the slope. If we just plug in the point (2,3) to the equation and solve then we will get:
As you can see, both methods give us the same equation of a line.