Unit 07 · Equations Inequalities and RelationshipsLesson

Day 102Dependent and Independent Variables

LearnClassworkAnswer keyPDF packet ↗
Standards 6.EE.C.9
LEARNING TARGET

I can identify quantities that change together and write a rule.

Build the idea

The independent variable is the input you choose; the dependent variable changes with it. Define both and write the output in terms of the input. A table and graph must show the same rule and units.

WORKED EXAMPLE 1

A shop charges $5 for each of n notebooks. Name the independent and dependent variables and write a cost rule.

Independent n = notebooks; dependent C = cost; C = 5n

The chosen notebook count is the input; multiply it by price and add any fixed fee to get the cost.

WORKED EXAMPLE 2

A shop charges $3 for each of n notebooks plus a single $6 delivery fee. Name the independent and dependent variables and write a cost rule. What does the cost at n = 0 mean in this model?

Independent n = notebooks; dependent C = cost; C = 3n + 6; C(0) = $6, the fee

The chosen notebook count is the input; multiply it by price and add any fixed fee to get the cost.

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. A shop charges $6 for each of n notebooks. Name the independent and dependent variables and write a cost rule.

  2. A shop charges $2 for each of n notebooks. Name the independent and dependent variables and write a cost rule.

  3. A shop charges $8 for each of n notebooks. Name the independent and dependent variables and write a cost rule.

  4. A shop charges $4 for each of n notebooks plus a single $3 delivery fee. Name the independent and dependent variables and write a cost rule.

  5. A shop charges $5 for each of n notebooks plus a single $3 delivery fee. Name the independent and dependent variables and write a cost rule.

  6. A shop charges $3 for each of n notebooks plus a single $4 delivery fee. Name the independent and dependent variables and write a cost rule.

  7. A shop charges $2 for each of n notebooks plus a single $5 delivery fee. Name the independent and dependent variables and write a cost rule. What does the cost at n = 0 mean in this model?

  8. A shop charges $3 for each of n notebooks plus a single $5 delivery fee. Name the independent and dependent variables and write a cost rule. What does the cost at n = 0 mean in this model?

  9. A shop charges $2 for each of n notebooks plus a single $2 delivery fee. Name the independent and dependent variables and write a cost rule. What does the cost at n = 0 mean in this model?

  10. A shop charges $4 for each of n notebooks plus a single $5 delivery fee. Name the independent and dependent variables and write a cost rule. What does the cost at n = 0 mean in this model?

Answers and reasoning

Reveal the teacher answer key
  1. Independent n = notebooks; dependent C = cost; C = 6n

    The chosen notebook count is the input; multiply it by price and add any fixed fee to get the cost.

  2. Independent n = notebooks; dependent C = cost; C = 2n

    The chosen notebook count is the input; multiply it by price and add any fixed fee to get the cost.

  3. Independent n = notebooks; dependent C = cost; C = 8n

    The chosen notebook count is the input; multiply it by price and add any fixed fee to get the cost.

  4. Independent n = notebooks; dependent C = cost; C = 4n + 3

    The chosen notebook count is the input; multiply it by price and add any fixed fee to get the cost.

  5. Independent n = notebooks; dependent C = cost; C = 5n + 3

    The chosen notebook count is the input; multiply it by price and add any fixed fee to get the cost.

  6. Independent n = notebooks; dependent C = cost; C = 3n + 4

    The chosen notebook count is the input; multiply it by price and add any fixed fee to get the cost.

  7. Independent n = notebooks; dependent C = cost; C = 2n + 5; C(0) = $5, the fee

    The chosen notebook count is the input; multiply it by price and add any fixed fee to get the cost.

  8. Independent n = notebooks; dependent C = cost; C = 3n + 5; C(0) = $5, the fee

    The chosen notebook count is the input; multiply it by price and add any fixed fee to get the cost.

  9. Independent n = notebooks; dependent C = cost; C = 2n + 2; C(0) = $2, the fee

    The chosen notebook count is the input; multiply it by price and add any fixed fee to get the cost.

  10. Independent n = notebooks; dependent C = cost; C = 4n + 5; C(0) = $5, the fee

    The chosen notebook count is the input; multiply it by price and add any fixed fee to get the cost.

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