Directly Proportional Relationships in Mathematics

The video tutorial explains the concept of direct proportionality using relatable examples like apple juice portions and the cost of apples. It demonstrates how to solve proportionality problems by identifying the constant of proportionality (K) and applying it to different scenarios. Advanced examples involving cubes and roots are also covered, providing a comprehensive understanding of the topic.

If one person at a party drinks two portions of apple juice, how many portions are needed for five people?

• 15 portions

• 10 portions

• 20 portions

• 5 portions

What does it mean when two quantities are directly proportional?

• One quantity decreases as the other increases.

• Both quantities remain constant.

• One quantity increases as the other increases by a constant factor.

• One quantity increases while the other decreases.

In the context of apple cost, if the cost is directly proportional to the number of apples, what is the equation form?

• C = a + K

• C = K - a

• C = a / K

• C = K * a

If the cost of 5 apples is $10, what is the constant of proportionality (K)?

• 1

• 2

• 3

• 4

Using the constant K = 2, what is the cost for 8 apples?

• $12

• $18

• $14

• $16

What does it mean when Y is directly proportional to the cube of X?

• Y = K * X

• Y = K * X^3

• Y = K / X^3

• Y = K * X^2

If Y = 48 when X = 2 and Y is directly proportional to X cubed, what is the value of K?

• 6

• 5

• 7

• 4

How would you express a directly proportional relationship involving the square root of a variable?

• A = K + B

• A = K / B

• A = K * sqrt(B)

• A = K * B^2