Finding The Slope of a Line Between Two Points

So far, we’ve found the slope of a line from a graph and from a table. Now let’s look at the formula we use to find the slope of a line between two points, represented by:

Remember that the slope formulas we’ve looked at so far are:

The last one is important, as it tells us the change in y divided by the change in x. Let’s look at an example:

Find the slope of the line between the points (1,5) and (3,8):

Here’s our new formula:

and this is the same as the above formulas that we’ve been using over the past few articles (it just looks ugly because of the superscripts, but I promise it's the same idea ;)

I’m going to pick

Let’s plug our values into the new equation:

Notice that if we graph the two points and find the slope from the graph, we get the same thing:

Notice, our vertical change is 3, and our horizontal change is 2, so we get the same slope as above! (Plug the vertical and horizontal change into the formulas above if you're not sure.)

Let’s try the same example, but instead we’re going to let

Do you think we’ll get a different slope?

We get the same slope! It doesn’t matter what direction we go in (just like when we worked with graphs and tables) we get the same slope.

Let’s try another example:

Find the slope of the line connecting the points (-1,4) and (-2, -1):

Let’s see what our new formula gives us:

If we switch the order of the points we get:

And we still get the same slope! That’s pretty much the main idea (*cough* formula) behind finding the slope between two points. Just be careful about adding/subtracting negatives and taking care of double negatives when they show up (like the one we just did.)

I hope this article helped with finding the slope between two points, good luck with your studies and have a great day!