The slope of a line on a graph is determined by calculating the ratio of the change in y-coordinate to change in x-coordinate for any two points on that line. In other words, the slope is ∆y/∆x.
 

Calculating the slope of a line does not have to be difficult. There are four simple steps that must be taken to do it.  Here are the steps:
 

1. Find the x, y coordinates of two points that lie on the line. In this Concept Builder, you can find these coordinate values by tapping on any of the six data points. The coordinates are displayed above the graph. Take the time to write these coordinates down in X, Y format. It might look something like this:
     (X₁, Y₁) = (3.0 s, 5.0 m)  and  (X₂, Y₂) = (6.0 s, 14.0 m)
    
2. Using the two sets of coordinates, calculate the change in the Y-coordinate value. We sometimes refer to this as the ∆Y or as the rise. It is an indicator of how high the line rises vertically between the two points. For the coordinates given in step 1, the ∆Y calculation would look like this:
     ∆Y = Y₂ - Y₁ = (14.0 m - 5.0 m) = 9.0 m
    
3. Using the same two sets of coordinates, calculate the change in the X-coordinate value. We sometimes refer to this as the ∆X or as the run. It is an indicator of how far the line runs horizontally between the two chosen points. For the coordinates given in Step 1, the ∆X calculation would look like this:
     ∆X = X₂ - X₁ = (6.0 s - 3.0 s) = 3.0 s
    
4. Determine the ratio of the change in Y to the change in X by dividing ∆Y value (from step 2) by the ∆X value (from step 3). For the set of two points provided as the example in Step 1, the calculation would go like this:
     Slope = ∆Y/∆X = (9.0 m) / (3.0 s) = 3.0 m/s

You might have noticed that the line on this graph slopes downward. Such a line has a negative slope. This should be the result of the calculations that you perform. You should receive a negative slope result when you do Step 4 of this 4-step procedure. You will have to enter the slope as a negative value.