Writing Algebraic Expressions for Direct Proportional Relationships

This video tutorial explains the concept of direct proportionality using examples such as hours worked and money earned, boiling water, and wire length and diameter. It demonstrates how to write equations to express these relationships and solve related problems by finding constants of proportionality.

What happens to one variable when the other increases in a direct proportional relationship?

• It fluctuates randomly

• It remains constant

• It decreases

• It increases proportionately

If 'e' represents money earned and 'h' represents hours worked, what is the equation for their relationship if the rate is 12 pounds per hour?

• e = 12 + h

• e = 12h

• e = h/12

• e = h - 12

How much money would you earn if you worked for 3 hours at a rate of 12 pounds per hour?

• 48 pounds

• 30 pounds

• 36 pounds

• 24 pounds

In the boiling water example, what does 't' represent?

• Thermal energy

• Time

• Temperature

• Total mass

What is the constant of proportionality 'k' if it takes 600 seconds to boil 200 grams of water?

• 4

• 2

• 3

• 5

Using the equation t = 3m, how long will it take to boil 450 grams of water?

• 1650 seconds

• 1350 seconds

• 1200 seconds

• 1500 seconds

What is the relationship between the length and diameter of a wire in the given example?

• Length is inversely proportional to diameter

• Length is directly proportional to diameter

• Length is equal to diameter

• Length is unrelated to diameter

If a wire is 25 cm long and has a diameter of 2 cm, what is the constant of proportionality 'k'?

• 20

• 15

• 12.5

• 10

Using the equation l = 12.5d, what is the diameter of a wire that is 40 cm long?

• 2.5 cm

• 3.2 cm

• 4 cm

• 5 cm

What is the final step to find the diameter of a wire using the equation l = 12.5d?

• Add 12.5 to both sides

• Divide both sides by 12.5

• Subtract 12.5 from both sides

• Multiply both sides by 12.5