INVERSE 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.

Does the table show an inverse variation?

• Yes

• No

Answer explanation

Yes, the table shows an inverse variation because as one variable increases, the other decreases, maintaining a constant product. This relationship confirms the presence of inverse variation.

Which equation represents inverse variation?

• y = x + ⅕

• y = (⅕) x + 5

• y = (⅕) x

• y = 5 / x

• y = 5 x

Answer explanation

The equation y = 5 / x represents inverse variation because it shows that as x increases, y decreases, and vice versa. This is the defining characteristic of inverse variation, unlike the other options.

Identify the inverse variation relationship from the following equations:

Answer explanation

The equation y=\frac{4}{x} represents an inverse variation because y varies inversely with x. As x increases, y decreases, which is characteristic of inverse relationships. The other equations do not exhibit this behavior.

If y varies inversely as x and x=5 when y=20, then what is the constant of variation, k? 

• 121

• 4

• 100

• 6

Answer explanation

Since y varies inversely as x, we have the relationship y = k/x. Given x = 5 and y = 20, we can find k: 20 = k/5, thus k = 20 * 5 = 100. Therefore, the constant of variation, k, is 100.

What is the constant (k) in this inverse variation?
y = 400/x

• x

• y

• 400

• Not enough information given

Answer explanation

In the equation y = 400/x, the constant k in inverse variation is the value that y multiplied by x equals. Here, k = 400, making the correct answer 400.

Given the following equation, identify the constant k.
y = 54/x

• k = 1/54

• k = x

• k = 54

• k = 1/x

Answer explanation

In the equation y = 54/x, the constant k is the coefficient of y when expressed in the form y = k/x. Here, k = 54, making the correct choice k = 54.

The width of a rectangle varies inversely with its length.  If the width is 6 when the length is 24, give an equation that shows the relationship.

• y= 4x

• y= 144x

• y= 4/x

• y= 144/x

Answer explanation

The width (w) varies inversely with the length (l), so w = k/l. Given w = 6 and l = 24, we find k = 6 * 24 = 144. Thus, the equation is w = 144/l, or y = 144/x, which is the correct choice.

x and y vary inversely. Given (5, 20), what is the constant k?

• 4

• 5

• 25

• 100

Answer explanation

Since x and y vary inversely, k = x * y. Given (5, 20), k = 5 * 20 = 100. Thus, the constant k is 100.

Boyle’s Law states that, for a fixed amount of gas, the volume of the gas at a constant   temperature is inversely proportional to the pressure. If a certain gas occupies 9.84 liters   at a pressure of 50 centimeters of mercury (cm Hg), what is the approximate pressure   when the volume is increased to 12 liters?

• 39.8 cm Hg

• 41.0 cm Hg 

• 43.2 cm Hg

• 45.1 cm Hg

Answer explanation

Using Boyle's Law (P1V1 = P2V2), we have P1 = 50 cm Hg, V1 = 9.84 L, and V2 = 12 L. Solving for P2 gives P2 = (P1 * V1) / V2 = (50 * 9.84) / 12 = 41.0 cm Hg, which is the correct answer.