Exploring Direct and Inverse Variation in Algebra

The video tutorial explains the concepts of direct, inverse, and joint variation. Direct variation is when two variables have a constant ratio, while inverse variation involves a constant product. Joint variation involves more than two variables. The tutorial provides examples and explains how to identify the type of variation from data. It concludes with finding the equation representing inverse variation.

What does it mean when we say y varies directly with x?

• y is equal to a constant multiple of x

• y is equal to the inverse of x

• y decreases as x increases

• y is independent of x

Which statement is true about direct variation?

• y decreases as x increases

• y is unrelated to x

• y is inversely proportional to x

• y increases as x increases

If x is tripled in a direct variation, what happens to y?

• y remains constant

• y is one-third

• y is halved

• y is tripled

In an inverse variation, if x is doubled, what happens to y?

• y is quadrupled

• y remains constant

• y is halved

• y is doubled

What is the mathematical representation of inverse variation?

• x / y = k

• x - y = k

• x + y = k

• x * y = k

What happens to y in an inverse variation when x is increased?

• y remains the same

• y decreases

• y becomes zero

• y increases

What does joint variation involve?

• A constant relationship between two variables

• A relationship with more than two variables

• A relationship with exactly two variables

• No relationship between variables

In the given data, as x increases from 1 to 3, what happens to y?

• y decreases from 12 to 4

• y increases from 12 to 24

• y increases from 12 to 36

• y remains constant at 12

What type of variation is demonstrated if x * y = 12 consistently?

• Direct variation

• Inverse variation

• No variation

• Joint variation

Which equation correctly represents the relationship where x * y = 12?

• x - y = 12

• x * y = 12

• x + y = 12

• x / y = 12