How to Calculate Slope

Now that you understand it, let's learn how to calculate slope.  GRADE-A will teach you the easiest way to find the slope of your line whether you are given a graph, 2 points, a table of values, or an equation.

Finding the Slope When You Have a Graph

When you have a graph, you first need to identify 2 points on the line.  Look at the line we have drawn in the figure below.  The arrows identify our two points.  Please note that you can pick any two points on the line (there are a lot to choice from) but we usually like to pick points that fit nicely on the grid so that our numbers are "nicer."

There are many more points that you could choose, but these work well. 

Also, please notice that the first point given is the y-intercept. 

  
First Point:  (0, 2)

Second Point:  (3, 4)

Now, we can calculate slope by going on a little journey from point one to point two.  From the first point, walk north until you are right next to the second point.  Then walk to the east.  Count your steps...

There is another way that you can calculate slope from a graph.  Take the two points that you found, (0, 2) & (3, 4), and use them in the slope formula given in the next section.

Finding the Slope When You Have 2 Points

When you have two points it is very important that you label the numbers correctly.  Check out how...

• x₁ means "the first x value" and x₂ means "the second x value"

• y₁ means "the first y value" and y₂ means the "second y value"

Example:                         

Once you have the points labeled, carefully substitute them into the formula.

Now that you have your fraction, you can leave the slope like that or you can convert it to the decimal 2.5.  Either answer is fine.

Please be aware that you may see the slope formula written in a couple different ways.  Do not be alarmed, you can calculate slope many different ways and they all give you the right answer!

Finding the Slope When You Have a Table

Choose any two points from the table - usually we just take the first two.  Label them the same way we did here.  Check out the figure below.

Now, all you have to do is plug the points into the slope formula.  Go ahead and try to do it on your own before you look below.

The slope should be 2.  Did you get that?  I bet you did!

Finding the Slope When You Have an Equation

Use your equation to generate two points.  The easiest way to do this is to form a T-Chart like the one below.

Equation:  y = 3x + 2

The T-Chart helped us to find two points that are a part of our line.  In this example we found the points (0, 2) & (1, 5).

Again, once you have your two points, we can calculate slope by following the procedure for when you are given 2 points.

You should have found your slope to be equal to 3.

Of course, if your equation is in slope-intercept form, the slope is the value next to x.  If your equation is not in slope-intercept form, you can solve for y and then the slope will be the number next to x.

y = 3x + 2 is in slope intercept form. 

The number next to x is the slope - so slope = 3.

Congratulations, you can now calculate slope!  What will you do next?  Why not take a look at graphing equations from slope-intercept form?

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