Chapter Review of Linear Relations
Chapter
Chapter 5
Section
Chapter Review of Linear Relations
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Solutions 18 Videos

Christina works part-time at a flower shop. She earns $9/h. Her pay varies directly with the time, in hours, she works.

a) Choose appropriate letters for variables. Make a table of values showing Christina’s pay for 0 h, 1 h, 2 h, and 3 h.

b) Graph the relationship.

c) Write an equation in the form y = kx.

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Q1

The Jung family travels 300 km to a relative’s home. The distance, d, in kilometres, varies directly with the time, t, in hours.

a) Find an equation relating d and t if d = 144 when t = 1.5. What does the constant of variation represent?

b) Use the equation to determine how long it will take the Jungs to reach their destination.

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2.40mins
Q2

The volume of soup varies directly with the volume of water used to prepare it. John uses 2.5 L of water to make 3.0 L of soup.

a) Explain why this relation is a direct variation.

b) Graph this relation.

c) What will happen to the graph if John uses 2.8 L of water to make 3.0 L of soup

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3.02mins
Q3

a) Copy and complete the table of values, given that y varies partially with x.

b) Identify the initial value of y and the constant of variation from the table.

c) Write an equation relating y and x in the form y = mx + b.

d) Graph the relation. Describe the graph.

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0.42mins
Q4

Identify each relation as a direct variation, a partial variation, or neither. Justify your answer.

a) \displaystyle y = x^2 + 5

b) \displaystyle A = 3d - 2

c) \displaystyle C = 2.5m

d) \displaystyle y = -8x + 1

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Q5

A new restaurant is having advertising flyers printed. The cost to design and lay out the flyer is $500. There is an additional cost of $0.15 per flyer printed.

a) Identify the fixed cost and the variable cost of this partial variation.

b) Write an equation representing this relationship.

c) Use your equation to determine the total cost of 500 flyers.

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1.43mins
Q6

Determine the slope.

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0.17mins
Q7a

Determine the slope.

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0.27mins
Q7b

Calculate the slope of each line segment.

a) AB

b) CD

c) EF

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1.01mins
Q8

a) Draw an example of a line segment with an endpoint (3, 5) and a slope of 0.

b) Draw an example of a line segment with an endpoint (-4, 1) and an undefined slope.

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1.12mins
Q9

A ladder reaches 2 m up a wall. The foot of the ladder is 0.4 m from the wall. For safety reasons, the slope should be between 6.3 and 9.5. Is this ladder within the safe range?

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0.48mins
Q10

The graph shows the average amount of food energy used by a 50-kg person while taking part in various activities.

Describe the slope of each activity as a rate of change.

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Q11

The hair on your head grows at a constant rate. The longest strands of Samira’s hair were 45 cm long on her 12th birthday. She decided not to cut her hair for 5 years and the longest strands grew to 106 cm. Graph the length of Samira’s hair over the 5-year period. What is the slope of the graph? Express it as a rate of change.

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Q12

Use first differences to determine whether each relation is linear or non-linear.

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Q13a

Use first differences to determine whether each relation is linear or non-linear.

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Q13b

Each tile measures 2 cm by 2 cm. Use first differences to determine whether the relationship between the length of the row of tiles and its area is linear or non-linear.

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1.03mins
Q14

a) Confirm that this relation is linear.

b) Calculate the slope.

c) Write a equation for the relation.

d) Graph the relation.

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Q15

The table shows the mass of propane fuel remaining in a barbecue tank.

a) Confirm that this relation is linear.

b) Graph this relation.

c) Find the slope and the vertical intercept of the graph. What do they represent?

d) Write an equation for the mass of propane fuel in terms of the time.

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Q16