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 Lesson Plan: Visualizing Slope on a Graph

Lesson Objectives

  • Plot points on a coordinate plane.
  • Understand how slope is represented on a graph.
  • Calculate the slope of a line given two points on a graph.

Standards

  • CCSS.MATH.CONTENT.8.EE.B.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.
  • CCSS.MATH.CONTENT.8.F.B.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Prerequisites

  • Understanding of the coordinate plane and how to plot points
  • Knowledge of the concept of slope (rise over run)
  • Familiarity with similar triangles and their properties

Materials

Warm Up Activity (5 minutes)

Review the concept of slope with a quick real-world example, such as the slope of a ramp or a hiking trail. Ask students to share their experiences with slopes in everyday life. 

Show these examples of stairs to compare steepness: https://www.media4math.com/library/75324/asset-preview

Explore (10 minutes)

Distribute graph paper and pencils to students. Provide them with a set of coordinates and ask them to plot the points on the coordinate plane. Then, have them connect the points to form a line. Encourage students to observe the steepness or flatness of the line they have drawn.

Review the following definitions:

Explain (10 minutes)

Demonstrate how to calculate the slope of a line given two points on a graph using the ratio of rise over run. Show this video to see how to do that.

https://www.media4math.com/library/75386/asset-preview

Use this Desmos activity to have students explore slope as the ratio of rise over run. Students click and drag on the two points and then use their understanding of right triangles to find the ratio of the rise over the run.

https://www.media4math.com/library/75385/asset-preview

Elaborate (5 minutes)

Use the Desmos activity from the previous section and have students find the slope for the line connecting the following pairs of points:

  • (0, 0) and (4, 4)
  • (1, 1) and (7, 4)
  • (2, 2) and (5, 8)
  • (0, 4) and (4, 0)

Have students click and drag on the points to place them on the proper coordinate. Or, if this is being presented to the class you can do this for them.

To calculate the slope have students:

  • Count the number of vertical spaces from one point to the other: This is the Rise.
  • Count the number of horizontal spaces from one point to the other: This is the Run.

Remind students:

  • The rise and the run are part of a right triangle where the line connecting the points is the hypotenuse. Show additional examples with both positive and negative slopes.
  • Lines with a positive slope point upward in going from left to right.
  • Lines with a negative slope point downward in going from left to right.

Evaluate (5 minutes)

Check for understanding with a quick 5-question quiz on identifying slope from a graph and calculating slope given two points. Include questions like:

  1. Which line has a positive slope?
    a) A line sloping upwards from left to right.
    b) A line sloping downwards from left to right.
    Answer: a
  2. Which line has a negative slope?
    a) A line sloping upwards from left to right.
    b) A line sloping downwards from left to right.
    Answer: b
  3. Calculate the slope of a line passing through the points (1, 2) and (4, 6).
    a) 1
    b) 2
    c) 3
    d) 4
    Answer: b
  4. Calculate the slope of a line passing through the points (-2, 3) and (4, -1).
    a) -1
    b) -2
    c) 1
    d) 2
    Answer: a
  5. If a line passes through the points (3, 5) and (3, 9), what is its slope?
    a) 0
    b) 1
    c) 2
    d) Undefined
    Answer: d

 

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