Understanding Inversely Proportional Relationships

The video tutorial explains the concept of inverse proportionality using the example of farmers picking apples. It describes how the time taken to pick apples decreases as the number of farmers increases, illustrating this relationship with graphs and algebraic equations. The tutorial also provides examples of calculations using the inverse proportionality equation and concludes with a summary of the key points.

What happens to the time taken to pick apples as the number of farmers increases?

• It increases.

• It decreases.

• It remains the same.

• It fluctuates randomly.

If the number of farmers doubles, what happens to the time taken to pick the apples?

• It halves.

• It quadruples.

• It doubles.

• It remains the same.

How is an inversely proportional relationship represented on a graph?

• As a straight vertical line.

• As a straight horizontal line.

• As a downward sloping curve.

• As an upward sloping curve.

In a graph of an inversely proportional relationship, what does a point in the top left represent?

• Many farmers and a short time taken.

• Few farmers and a short time taken.

• Many farmers and a long time taken.

• Few farmers and a long time taken.

What does the equation t ∝ 1/f represent?

• Time taken is directly proportional to the number of farmers.

• Time taken is inversely proportional to the number of farmers.

• Time taken is equal to the number of farmers.

• Time taken is unrelated to the number of farmers.

What is the purpose of the constant of proportionality (k) in the equation t = k/f?

• To ensure the equation is always equal to zero.

• To eliminate the need for variables.

• To convert the proportional relationship into an equation.

• To make the equation more complex.

If k = 8 and there are 2 farmers, how long will it take to pick the apples?

• 2 hours

• 4 hours

• 8 hours

• 16 hours

If k = 8 and there are 5 farmers, how long will it take to pick the apples?

• 1.6 hours

• 8 hours

• 2 hours

• 4 hours

What does it mean if one variable is equal to something over another variable?

• The variables are unrelated.

• The variables are equal.

• The variables are inversely proportional.

• The variables are directly proportional.

Which of the following is an example of an inversely proportional relationship?

• y = 2x

• y = x + 2

• y = 2/x

• y = x - 2