Inverse Variation Equations Identify

The cost per person (C) to rent a mountain cabin is inversely proportional to the number of people (P) who share the rent. If the cost per person is $36 when 5 people share, what is the cost per person when 8 people share?

• $22.50

• $57.60

• $1.11

• $12.50

Answer explanation

The cost per person (C) is inversely proportional to the number of people (P), so C = k/P. With C = 36 when P = 5, k = 180. For P = 8, C = 180/8 = 22.50. Thus, the cost per person when 8 people share is $22.50.

Given that y varies inversely with x, if x =7 and y = 4, what is y when x = 2?

• 14

• 10

• 2

• -14

Answer explanation

Since y varies inversely with x, we have the relationship y = k/x. Given x = 7 and y = 4, we find k = 28. When x = 2, y = 28/2 = 14. Thus, the correct answer is 14.

If a varies inversely as b, and a = 32 when b = 3, find b when a = 15.

• 3/5

• 8/5

• 16/5

• 32/5

Answer explanation

Since a varies inversely as b, we have a * b = k. Given a = 32 and b = 3, k = 32 * 3 = 96. Now, for a = 15, we find b: 15 * b = 96, so b = 96/15 = 32/5. Thus, the correct answer is 32/5.

Assume y varies inversely with x. What is the equation that best represents the relationship?

• y = 12/x

• y = 1/2x

• y = 6x

• y = -20/x

State what type of variation the equation represents.

• Direct

• Inverse

• Joint

• None

The image is an example of the graph of a(n)

• direct variation

• inverse variation

• neither

• both

Which of the following is the equation format for inverse variation?

• y = mx + b

• y = kx

• xy=k

What kind of equation is this?
xy=8

• Linear Equation

• Direct Variation

• Inverse Variation

• Joint Variation

What kind of equation is this?
xy = -18

• Linear Equation

• Direct Variation

• Inverse Variation

• Joint Variation

Which of the statements BEST describes an inverse variation?

• an increase in x causes a decrease in y

• an increase in x causes an increase in y

Answer explanation

An inverse variation means that as one variable increases, the other decreases. Therefore, the correct statement is that an increase in x causes a decrease in y, which accurately describes the relationship in inverse variation.