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Cogito

Grade 8 Math · Chapter 3 · Lesson 1

Practice Worksheet

Why Slope Is the Same Everywhere

The similar triangles you just built.

10 problems · about 19 minutes · 8.EE.B.6

NameDate

Figure — use these to answer the problems

Two slope triangles of different sizes. Compare their ratios.
-10-10-5-55510101236
y = 2x + 1
Slope2
Where it crosses1
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Angle-Angle Similarity”

    Angles 25° and 95°. What is the third?

    Answer

  2. From “Dilations on the Coordinate Plane”

    (4, −3) dilated by 5. What is the new y?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Rise 12, run 4. Slope?

    Answer

  2. Why is slope the same everywhere on a line?

    • The slope triangles are similar, so their sides share one ratio.
    • Because that is the definition.

  3. Rise 10, run 5. Slope?

    Answer

  4. Rise 3, run 6. Slope, as a decimal?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. Falls 9 over a run of 3. Slope?

    Answer

  2. What is the slope of a horizontal line?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

2 problems

  1. The Slope

    A line rises 6 for a run of 2. What is its slope?

    Answer

  2. Going Down

    A line falls 8 over a run of 4. What is its slope?

    Answer