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Cogito

Grade 8 Math · Chapter 3 · Lesson 4

Practice Worksheet

Unit Rate as Slope

The rate is the steepness.

10 problems · about 18 minutes · 8.EE.B.5

NameDate

Figure — use these to answer the problems

Set the rate. A steeper line means more y for every one across.
-10-10-5-5551010
y = 3x
Rate, in units per hour3
Where it crosses0
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

3 problems

  1. From “Slope from Two Points”

    Through (1, 2) and (4, 11). Slope?

    Answer

  2. From “y = mx + b”

    y = 3x − 4. What is y when x = 6?

    Answer

  3. From “Why Slope Is the Same Everywhere”

    Rise 12, run 4. Slope?

    Answer

Warm Up

Straightforward practice. Get the method working first.

3 problems

  1. A proportional line through (7, 28). What is its slope?

    Answer

  2. Through (3, 15). Slope?

    Answer

  3. 6 kg costs £30. Rate in pounds per kg?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. Of slopes 3 and 7, which line is steeper? Give the number.

    Answer

  2. A proportional line through (5, 20). What is y when x is 1?

    Answer

Stretch Yourself

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

2 problems

  1. The Table

    5 hours earns £40. What is the rate, in pounds per hour?

    Answer

  2. The Graph

    A proportional line passes through (4, 36). What is its slope?

    Answer