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?

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.

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

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‘.

Which relations are a direct variation? Why?

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.

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?

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

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

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

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