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Constant of Proportionality

Constant of Proportionality. Try It!. Liam took his dog for a walk. In 4 minutes, he had walked 2 blocks. In 10 minutes, he had walked 5 blocks. If the number of blocks is proportional to the number of minutes, what is the constant of proportionality for the relationship?. Talk About It.

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Constant of Proportionality

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  1. Constant of Proportionality

  2. Try It! • Liam took his dog for a walk. In 4 minutes, he had walked 2 blocks. In 10 minutes, he had walked 5 blocks. If the number of blocks is proportional to the number of minutes, what is the constant of proportionality for the relationship?

  3. Talk About It • Graph the relationship on the pegboard. Put distance on the y-axis and time on the x-axis. • What two points will you graph? • Can you confirm that the relationship is proportional? • What is the horizontal distance between the two points? • What is the vertical distance between the two points? (You should have a right triangle.)

  4. Talk About It • Divide the vertical distance by the horizontal distance. • The quotient is called the “constant of proportionality.” • It is also called the “unit rate” because it tells how much the y-coordinate changes for each unit of change in the x-coordinate.

  5. Talk About It • The problem says the number of blocks is proportional to the number of minutes, so the number of blocks goes on the y-axis and time goes on the x-axis. • The unit rate will be the same regardless of what two points are chosen from the line. • Which point on the line will give you the unit rate directly, without having to calculate?

  6. Solve It • Based on the problem, draw a graph on grid paper. Identify the vertical distance and the horizontal distance of the two given points. Show how you divide to find the constant of proportionality. Identify on the graph the unit rate without calculating.

  7. Check for Understanding • Teo has 3 trophies and 6 medals. Brandi has 5 trophies and 10 medals. If the number of medals is proportional to the number of trophies, which point will be on the graph of this relationship? • A. (0,1) B. (1,2) C. (4,7) D. (12,5)

  8. Practice and Homework • Start on Lesson 3 Constant of Proportionality worksheet. Read the directions carefully. • Homework: Complete worksheet and look at the web page for additional problems for practice.

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