Understanding Constant of Proportionality

This video tutorial introduces the concept of constant of proportionality through various word problems. It explains how to set up and solve problems using ratios and proportions, focusing on real-world examples like car mileage, map scales, and evaporation rates. The tutorial emphasizes understanding the constant of proportionality as a fixed ratio between two related quantities, regardless of the specific values involved.

What is the constant of proportionality in the car mileage problem if Regina can travel 180 miles on 6 gallons of gas?

• 35 miles per gallon

• 30 miles per gallon

• 25 miles per gallon

• 20 miles per gallon

If Regina uses 5 gallons of gas, how far can she travel?

• 200 miles

• 180 miles

• 150 miles

• 120 miles

In the map scale problem, what is the constant of proportionality if 2 inches on the map represent 5 miles in reality?

• 3/5 inches per mile

• 4/5 inches per mile

• 2/5 inches per mile

• 1/5 inches per mile

How many inches on the map represent 15 miles in reality?

• 4 inches

• 7 inches

• 5 inches

• 6 inches

For the commercial time problem, how many seconds of airtime can be purchased for $300?

• 80 seconds

• 90 seconds

• 70 seconds

• 60 seconds

What is the constant of proportionality in the commercial time problem?

• 4/10 seconds per dollar

• 3/10 seconds per dollar

• 2/10 seconds per dollar

• 1/10 seconds per dollar

In the water evaporation problem, how many days will it take for 7 centimeters to evaporate?

• 26 days

• 24 days

• 30 days

• 28 days

What is the constant of proportionality in the water evaporation problem?

• 2 days per centimeter

• 5 days per centimeter

• 3 days per centimeter

• 4 days per centimeter

If the pool loses 2 centimeters of water every 8 days, how many centimeters will evaporate in 16 days?

• 2 centimeters

• 3 centimeters

• 4 centimeters

• 5 centimeters

What is the key takeaway about the constant of proportionality from this lesson?

• It varies with the type of problem.

• It is only applicable to distance problems.

• It remains constant regardless of the quantities involved.

• It changes with different quantities.