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Cogito

Grade 8 Math · Chapter 6 · Lesson 3

Practice Worksheet

Rate of Change and Starting Value

Building a function from a situation.

10 problems · about 19 minutes · 8.F.B.4

NameDate

Figure — use these to answer the problems

Set a rate and a starting value and read the function they describe.
-10-10-5-5551010
y = 3x + 2
Rate of change3
Starting value2
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

3 problems

  1. From “Linear and Nonlinear Functions”

    4, 10, 16, 22. Constant rise?

    Answer

  2. From “What a Function Is”

    Rule "multiply by 4 then add 1". What comes out when 5 goes in?

    Answer

  3. From “Solving a System by Elimination”

    x + y = 12 and x − y = 4. What is x?

    Answer

Warm Up

Straightforward practice. Get the method working first.

3 problems

  1. Through (0, 7) and (3, 19). What is the rate?

    Answer

  2. Starts at 6, rises 2 each step. What is y at x = 4?

    Answer

  3. y = 5x + 3. What is the starting value?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. Through (0, 4) and (2, 10). What is the rate?

    Answer

  2. y = −2x + 20. What is y at x = 5?

    Answer

Stretch Yourself

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

2 problems

  1. The Tank

    y = −4x + 50. How many litres after 10 minutes?

    Answer

  2. The Empty Tank

    y = −4x + 50. After how many minutes is it empty?

    Answer