Direct Proportionality Concepts

The video tutorial explains the concept of direct proportion, where one variable increases as another does. It introduces the proportional symbol and how to convert it into an equation using a constant of proportionality. The tutorial provides examples of direct proportion with variables, including direct proportion to X, the square of X, the cube of X, and the square root of X. Each example demonstrates how to find the constant of proportionality and solve for unknowns using the derived formula.

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

• The variables are unrelated.

• As one variable increases, the other also increases.

• As one variable increases, the other remains constant.

• As one variable increases, the other decreases.

What symbol is used to denote direct proportion?

• Multiplication sign

• Division sign

• Proportional symbol

• Equal sign

If Y is directly proportional to X and Y = 20 when X = 5, what is the constant of proportionality?

• 2

• 3

• 5

• 4

In the equation Y = kX, what does 'k' represent?

• The variable

• The difference between X and Y

• The constant of proportionality

• The sum of X and Y

If Y is directly proportional to the square of X, and Y = 5 when X = 4, what is the value of Y when X = 8?

• 10

• 25

• 15

• 20

What is the formula for Y when it is directly proportional to the square of X?

• Y = kX^3

• Y = k√X

• Y = kX^2

• Y = kX

If Y is directly proportional to X cubed, and Y = 40 when X = 2, what is the constant of proportionality?

• 4

• 3

• 2

• 5

How do you find X if Y is directly proportional to X cubed and Y = 800?

• Multiply Y by the constant of proportionality and take the square root

• Divide Y by the constant of proportionality and take the cube root

• Divide Y by the constant of proportionality and take the square root

• Multiply Y by the constant of proportionality and take the cube root

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

• 2.0

• 1.5

• 1.2

• 1.0

What is the value of X if Y is directly proportional to the square root of X, Y = 36, and the constant of proportionality is 1.2?

• 900

• 600

• 400

• 800