4.7 Chapter 4 Review
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Solutions 11 Videos

House Painting Pros charge $100 plus $250 per room.

a) Make a table of values to show the price of painting up to 5 rooms. b) Graph this relation.

c) Describe the relation represented by the graph.

d) What would the price be to paint a home with 8 rooms?

e) How many rooms can be painted for $1100?

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Q1

Make a graph of each relation and explain why it is linear.

a) The cost to produce a newsletter is $500 plus $0.40 for each copy.

b) The temperature is dropping by 2 ^oC per hour, from an initial temperature of 18 °C.

c) The cost of a lawn cutting service is $5.50 per square metre.

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Q2

Calculate the rate of change for each interval. 1s the relation linear?

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Q3

A graphic designer charges $100 plus $40/hour to design a logo.

a) Which number is the rate of change?

b) Calculate the cost for a logo that takes

  • 3 hours to design
  • 5 hours to design
  • 10 hours to design

c) Calculate the rates of change between 3 and 5 hours, and between S and 10 hours. d) Doestherateofchangeoverthetwotimespansin'partc)change or remain' constant? Explain‘.

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Q4

Which relations are a direct variation? Why?

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Q5

A cell phone plan is advertised at $25.99 per month.

a) Is this an example of direct variation? If so, state thev ariables

  • the initial value
  • the rate of change
  • an equation representing the relation

b) Explain how to use the equation. Use an example to help you.

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Q6

a) What 15‘ the rate of change? What does it represent? b) State an equation representing' this relation. c) What is the cost to download

  • 2 songs?
  • 20 songs?
  • 200 songs?
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Q7

Classify each graph as a direct variation, a partial variation, or neither. Justify your answer.

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Q8

A company makes laser~engraved crystals to sell as souvenirs. It charges $100 for the laser setup and $12 per crystal.

a) Is this a direct or partial variation? Explain.

b) Write an equation representing this relation.

e) Use your equation to determine the cost of 200 laser-engraved crystals

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Q9

At a collectibles fair, Danny sells comic books for $25 each.

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Q10

The equation P = -100 + 10n represents the profit, P, in dollars, that Danny makes when he sells n comic books at collectibles fair.

Represent this relation and the rate of change in three ways:

  • in words
  • in a table of values
  • graphically
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Q11