Lesson 10

Meet Slope

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Problem 1

Of the three lines in the graph, one has slope 1, one has slope 2, and one has slope \(\frac{1}{5}.\) Label each line with its slope.

Three lines on a grid. The black line begins at 0 comma 5 & rises 1 vertical unit for each 5 horizontal units. The yellow line at 0 comma 3, the blue line begins at 0 comma 8. They meet at 5 comma 13.

Solution

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Problem 2

Draw three lines with slope 2, and three lines with slope \(\frac 1 3\). What do you notice?

Blank grid, 14 blocks wide, 11 blocks high.

Solution

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Problem 3

The figure shows two right triangles, each with its longest side on the same line.

Two triangles. First horizontal side length 4, vertical side length 2, Second horizontal side length 6, vertical side length 3.
  1. Explain how you know the two triangles are similar.
  2. How long is \(XY\)?
  3. For each triangle, calculate (vertical side) \(\div\) (horizontal side).
  4. What is the slope of the line? Explain how you know.

Solution

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Problem 4

Triangle \(A\) has side lengths 3, 4, and 5. Triangle \(B\) has side lengths 6, 7, and 8.

  1. Explain how you know that Triangle \(B\) is not similar to Triangle \(A\).

  2. Give possible side lengths for Triangle \(B\) so that it is similar to Triangle \(A\).

Solution

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(From Unit 2, Lesson 9.)