Proportional Relationships and Functions

The video tutorial explains the concept of direct proportion, where two variables increase together. It introduces the proportional symbol and how to express direct proportion using a formula. The tutorial provides examples of direct proportion, including cases where one variable is proportional to the square, cube, or square root of another variable. Each example demonstrates how to find the constant of proportionality and solve for unknown values.

What does it mean when two variables are in direct proportion?

• The variables are unrelated.

• As one variable increases, the other also increases.

• Both variables remain constant.

• As one variable increases, the other decreases.

Which symbol is used to denote proportionality?

• Multiplication sign

• Equal sign

• Infinity symbol

• Proportional symbol

How can the equation 'a is proportional to b' be expressed?

• a = b + k

• a = b / k

• a = b - k

• a = k * b

In the first example, if Y is directly proportional to X and Y = 20 when X = 5, what is the constant of proportionality?

• 4

• 3

• 2

• 5

Using the formula Y = 4X, what is Y when X = 15?

• 45

• 55

• 50

• 60

In the second example, Y is directly proportional to the square of X. If Y = 5 when X = 4, what is the constant of proportionality?

• 3/4

• 5/16

• 1/4

• 1/2

Using the formula Y = 0.3125X², what is Y when X = 8?

• 18

• 24

• 20

• 22

In the third example, Y is directly proportional to X cubed. If Y = 40 when X = 2, what is the constant of proportionality?

• 4

• 6

• 5

• 7

Using the formula Y = 5X³, what is X when Y = 800?

• 7.43

• 6.43

• 5.43

• 4.43

In the fourth example, Y is directly proportional to the square root of X. If Y = 12 when X = 100, what is the constant of proportionality?

• 1.3

• 1.2

• 1.1

• 1.0