Inverse Variation Worksheet

**Page 1**

1.

If the point (7, 15) is from an inverse variation, then find the constant of variation.

a. | $\frac{7}{8}$ | ||

b. | 105 | ||

c. | 107 | ||

d. | $\frac{1}{105}$ |

So, the value of

Correct answer : (2)

2.

Find the constant of variation if the relationship among the data in the table is an inverse variation.

$x$ | 0.15 | 0.25 | 0.35 |

$y$ | 70 | 42 | 30 |

a. | 1.05 | ||

b. | 5.01 | ||

c. | 10.5 | ||

d. | 466.67 |

(0.15) (70) = 10.5

(0.25) (42) = 10.5

(0.35) (30) = 10.5.

[Find the product

The product

So, constant of variation is 10.5.

Correct answer : (3)

3.

Determine whether the relationship among the data in the table is an inverse variation, if so find the constant of variation.

$x$ | 2 | - 3 | 4 |

$y$ | 0.25 | - 0.375 | 0.5 |

a. | No | ||

b. | Yes, 2 | ||

c. | Yes, 0.5 | ||

d. | Yes, 1.125 |

(2) (0.25) = 0.5 (- 3) (- 0.375) = 1.125 (4) (0.5) = 2.

[Find the product

The product

Correct answer : (1)

4.

Write an equation to model the data given in the table:

$x$ | 2.4 | 2.6 | 2.8 |

$y$ | 4.55 | 4.2 | 3.9 |

a. | $\frac{x}{y}$ = 10.92 | ||

b. | $\mathrm{xy}$ = 10.92 | ||

c. | there is no relation between $x$ and $y$. | ||

d. | $\frac{y}{x}$ = 10.92 |

An inverse variation is a linear function that can be written in the form

(2.4) (4.55) = 10.92 (2.6) (4.2) = 10.92 (2.8) (3.9) = 10.92

[Find the product

The product

The equation is

Correct answer : (2)

5.

A gas exerts a pressure of 76 pounds per square inch when its volume is 40 cubic feet. What is the pressure exerted by the gas when its volume is 95 cubic feet assuming that the product of pressure and volume is constant?

a. | 37 pounds per square inch | ||

b. | 32 pounds per square inch | ||

c. | 96 pounds per square inch | ||

d. | 34 pounds per square inch |

(76)(40) = K

[Substitute the values.]

So, K = 3040

Now the equation is P =

P =

[Substitute V = 95 cubic feet.]

P = 32

The gas at a volume of 95 cubic feet exerts a pressure of 32 pounds per square inch.

Correct answer : (2)

6.

Given $\mathrm{xy}$ = 19 , then find the values of $a$, $b$ and $c$ in the table.

$x$ | $y$ |

10 | $a$ |

$b$ | 19 |

9 | $c$ |

a. | $a$ = 2.1, $b$ = 1.9, $c$ = 1 | ||

b. | $a$ = 1.9, $b$ = 1, $c$ = 9 | ||

c. | $a$ = 1.9, $b$ = 19, $c$ = 2.1 | ||

d. | $a$ = 1.9, $b$ = 1, $c$ = 2.1 |

From the table, substitute

10 | ( | 9 |

| | |

| | |

Correct answer : (4)

7.

If the point (2.76, 7.29) is from an inverse variation, then write an equation to model the data.

a. | $\mathrm{xy}$ = 20.71 | ||

b. | $\mathrm{xy}$ = 21.12 | ||

c. | $\frac{x}{y}$ = 19.12 | ||

d. | $\mathrm{xy}$ = 20.12 |

So, the constant of variation

The equation is

Correct answer : (4)

8.

If ($x$, $g$) and ($t$, $d$) both satisfy an inverse variation, then which of the following relation is true?

a. | $\frac{x}{t}$ = $\frac{d}{g}$ | ||

b. | $\frac{t}{x}$ = $\frac{g}{d}$ | ||

c. | $\mathrm{xg}$ = $\mathrm{td}$ | ||

d. | All the above |

Substitute (

Substitute (

So,

[Divide throughout by

[Divide throughout by

Correct answer : (4)

9.

If the pair of points (8, 2) and (- 4, $y$) are from an inverse variation, then find the value of $y$.

a. | - $\frac{17}{4}$ | ||

b. | - $\frac{15}{4}$ | ||

c. | - 4 | ||

d. | - $\frac{16}{3}$ |

So,

(8)(2) = (- 4)(

16 = - 4

Correct answer : (3)

10.

Given $\mathrm{xy}$ = 2.5 , then find the values of $a$, $b$ and $c$ in the table:

$x$ | $y$ |

$a$ | 0.149 |

0.215 | $b$ |

$c$ | 5 |

a. | $a$ = 16.8, $b$ = 11.6, $c$ = 0.5 | ||

b. | $a$ = 0.149, $b$ = 0.215, $c$ = 5 | ||

c. | $a$ = 0.1, $b$ = 0.1, $c$ = 0.5 | ||

d. | $a$ = 16.8, $b$ = 11.6, $c$ = 5 |

From the table, substitute

( | (0.215) ( | ( |

| | |

| | |

Correct answer : (1)