Illustrative Mathematics Grade 8, Unit 3, Lesson 10: Calculating Slope

Learning Targets:

  • I can calculate positive and negative slopes given two points on the line.
  • I can describe a line precisely enough that another student can draw it.

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Illustrative Math
Grade 8

Lesson 10: Calculating Slope

Let’s calculate slope from two points.

Illustrative Math Unit 8.3, Lesson 10 (printable worksheets)

Lesson 10 Summary

The following diagram shows how to calculate slope from two points.
Calculate Slope

Lesson 10.1 Integer Operations Review

Find values for a and b that make each side have the same value.

Lesson 10.2 Toward a More General Slope Formula

  1. Plot the points (1,11) and (8,2), and use a ruler to draw the line that passes through them.
  2. Without calculating, do you expect the slope of the line through (1,11) and (8,2) to be positive or negative? How can you tell?
  3. Calculate the slope of this line.

Are you ready for more?

Find the value of k so that the line passing through each pair of points has the given slope.

  1. (k,2) and (11,14), slope = 2
  2. (1,k) and (4,1), slope = -2
  3. (3,5) and (k,9), slope = 1/2
  4. (-1,4) and (-3,k), slope = -1/2
  5. (-15/2,3/16) and (-13/22,k), slope = 0

Lesson 10.3 Travel Habits in July

Your teacher will give you either a design or a blank graph. Do not show your card to your partner.
If your teacher gives you the design:

  1. Look at the design silently and think about how you could communicate what your partner should draw. Think about ways that you can describe what a line looks like, such as its slope or points that it goes through.
  2. Describe each line, one at a time, and give your partner time to draw them.
  3. Once your partner thinks they have drawn all the lines you described, only then should you show them the design.
    If your teacher gives you the blank graph:
  4. Listen carefully as your partner describes each line, and draw each line based on their description.
  5. You are not allowed to ask for more information about a line than what your partner tells you.
  6. Do not show your drawing to your partner until you have finished drawing all the lines they describe.
    When finished, place the drawing next to the card with the design so that you and your partner can both see them. How is the drawing the same as the design? How is it different? Discuss any miscommunication that might have caused the drawing to look different from the design.
    Pause here so your teacher can review your work. When your teacher gives you a new set of cards, switch roles for the second problem.

Lesson 10 Practice Problems

  1. For each graph, calculate the slope of the line.
  2. Match each pair of points to the slope of the line that joins them.
  3. Draw a line with the given slope through the given point. What other point lies on that line?
  4. Make a sketch of a linear relationship with a slope of 4 and a negative y-intercept. Show how you know the slope is 4 and write an equation for the line.

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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