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Home Concept Builders Fundamentals: Relationships and Graphs Calculating Slope Help Help 3

Calculating Slope - Questions 3 Help

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.

There are two nearly identical versions of this question. Here is one of those versions:
 

Version 1:

Calculate the slope of the line on the graph.

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

In this question, the line on the graph passes through the origin. In step 1 of this 4-step process, it would be wise to use the origin as one of the chosen points. For instance, you could say that (X1, Y1) = (0.0 s, 0.0 m). Doing so will make the mathematics of this problem considerably easier.

Try this link to The Physics Classroom Tutorial for more help with Calculating Slope:

Determining the Slope of a Position-Time Graph

Concept Builder Teacher Notes Directions