Illustrative Mathematics Grade 8, Unit 2, Lesson 10: Meet Slope

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Illustrative Math
Grade 8

Lesson 10: Meet Slope

Let’s learn about the slope of a line.

Illustrative Math Unit 8.2, Lesson 10 (printable worksheets)

Lesson 10 Summary

The following diagram shows how to find the slope of a line on a grid.

Lesson 10.1 Equal Quotients

Write some numbers that are equal to 15 ÷ 12.

• See Video for Whole Lesson

Lesson 10.2 Similar Triangles on the Same Line

1. The figure shows three right triangles, each with its longest side on the same line.
   Your teacher will assign you two triangles. Explain why the two triangles are similar.
2. Complete the table.

Lesson 10.3 Multiple Lines with the Same Slope

Open Applet

1. Draw two lines with slope 3. What do you notice about the two lines?
2. Draw two lines with slope 1/2. What do you notice about the two lines?

Are you ready for more?

As we learn more about lines, we will occasionally have to consider perfectly vertical lines as a special case and treat them differently. Think about applying what you have learned in the last couple of activities to the case of vertical lines. What is the same? What is different?

Lesson 10.4 Different Slopes of Different Lines

Here are several lines.

1. Match each line shown with a slope from this list: 1/2, 2, 1, 0.25, 3/2, 1/2.
2. One of the given slopes does not have a line to match. Draw a line with this slope on the empty grid (F).

Lesson 10 Practice Problems

1. Of the three lines in the graph, one has slope 1, one has slope 2, and one has slope 1/5. Label each line with its slope.
2. Draw three lines with slope 2, and three lines with slope 1/3. What do you notice?
3. The figure shows two right triangles, each with its longest side on the same line.
   a. Explain how you know the two triangles are similar.
   b. How long is XY?
   c. For each triangle, calculate (vertical side) ÷ (horizontal side).
   d. What is the slope of the line? Explain how you know.
4. Triangle A has side lengths 3, 4, and 5. Triangle B has side lengths 6, 7, and 8.
   a. Explain how you know that Triangle B is not similar to Triangle A.
   b. Give possible side lengths for Triangle B so that it is similar to Triangle A.

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

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