Direct and Inverse Proportionality

y is directly proportional to x, and y = 24 when x = 4.

What is the value of y when x = 3?

• 18

• 20

• 23

• 43

The circumference (C cm) of a circle is directly proportional to its diameter (d cm).

The circumference of a circle of diameter 3.5 cm is 11 cm

What is the circumference of a circle of diameter 4.2 cm?

• 9.17 cm

• 11.7 cm

• 13.2 cm

• 14 cm

P is directly proportional to T.

Which of the following could be the graph connecting T and P?

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• 
• 
• 

y is inversely proportional to x, and y = 8 when x = 3

What is the value of y when x = 4?

• 6

• 7

• 9

• 10.67

The time (t days) required to build a house is inversely proportional to the number of builders (n), all working at the same rate.

If there are 6 builders, it takes 80 days to complete the house.

How many builders must be employed to build the house in just 16 days?

• 1.2 builders

• 25 builders

• 30 builders

• 36 builders

R is inversely proportional to I.

Which of the following could be the graph connecting I and R?

• 
• 
• 
• 

John and Karen both insure their properties with the Budget Insurance Company.

The cost of house insurance premiums with the Budget Insurance Company is directly proportional to the value of the property being insured.

John pays premiums of $76 per month on his property valued at $152,000

How much does Karen pay on her property valued at $259,000?

• $44.60

• $129.50

• $183.00

• $205.50

The amount of sales tax on a new car is directly proportional to the purchase price of the car.

Victor bought a new car for $30,000 and paid $1,500 in sales tax.

Wesley bought a new car from the same dealer and paid $2,375 sales tax.

How much did Wesley pay for his car?

• $18,947

• $30,875

• $45,000

• $47,500

The cost of insurance on a house is directly proportional to the area of the house.

Alan has a 2,500 square-foot house and pays a monthly insurance premium of $67.50

Bella has a 3,800 square-foot house insured with the same company. What is her monthly premium?

• $44.41

• $80.50

• $102.60

• $120.60

The stopping distance (d meters) of a car is directly proportional to the square of its speed (s km/h) when the brakes are applied.

A car travelling at 50 km/h requires a stopping distance of 20 meters.

If the stopping distance is 51.2 meters, what is the speed of the car when the brakes are applied?

HINT. directly proportional to the SQUARE

• 19.5 km/h

• 80 km/h

• 81.2 km/h

• 128 km/h