Direct Variation Worksheet

**Page 1**

1.

A soap manufacturing company packs 52 soaps per carton. Find the number of soaps that can be packed in 10 cartons, using a direct variation model.

a. | 468 | ||

b. | 624 | ||

c. | 572 | ||

d. | 150 |

Since, the number of soaps and the number of cartons vary directly, the equation is of the form

As each carton contains 52 soaps, the constant of variation is 52.

[Substitute the values.]

[Substitute the values.]

[Multiply.]

So, 150 soaps can be packed in 10 cartons.

Correct answer : (4)

2.

Which one of the following is not a direct variation?

a. | The amount of gas a person buys and the money he pays | ||

b. | Profit and sales | ||

c. | Circumference of a circle and its diameter | ||

d. | A person′s age and his height |

Correct answer : (4)

3.

If the circumference of a circle varies directly as its diameter, then the constant of variation is

a. | 3π | ||

b. | 2π | ||

c. | 4π | ||

d. | π |

= π

[

So, the constant of variation is π.

Correct answer : (4)

4.

Determine whether the graph represents a direct variation or not.

a. | no | ||

b. | yes |

So, the graph represents a direct variation.

Correct answer : (2)

5.

For the given function, find its equation if $y$ varies directly as $x$.

$x$ | $y$ |

9 | - 27 |

- 10 | 30 |

- 11 | 33 |

a. | $y$ = - 3$x$ | ||

b. | $y$ = $\frac{1}{3}$$x$ | ||

c. | $y$ = 5$x$ | ||

d. | $y$ = 31$x$ |

So,

The constant of variation is - 3.

So, the equation is

Correct answer : (1)

6.

Determine whether $y$ varies directly as $x$, if so, write its equation.

.

$x$ | $y$ |

6 | 8 |

8 | 6 |

11 | 2 |

a. | $y$ = ($\frac{6}{8}$)$x$ | ||

b. | $y$ = 0.6$x$ | ||

c. | $y$ does not vary directly as $x$ | ||

d. | $y$ = 1.33 $x$ |

Since the ratio

Correct answer : (3)

7.

Find the slope of the direct variation $y$ = ($\frac{2}{3}$)$x$.

a. | - $\frac{3}{2}$ | ||

b. | 2 | ||

c. | 3 | ||

d. | $\frac{2}{3}$ |

Constant of variation =

The slope of a direct variation has the same value as its constant of variation

Therefore, the slope of the given direct variation is

Correct answer : (4)

8.

A car runs 18 mi. on 2 gallons of gas. The number of gallons of gas varies directly with the number of miles the car runs. How many miles will the car run on 4.4 gallons of gas?

a. | 39.6 mi. | ||

b. | 2 mi. | ||

c. | 9 mi. | ||

d. | 18 mi. |

The relation is

[Direct variation.]

Let (

[Write a proportion.]

[Replace

[Simplify.]

So, the car runs 39.6 mi. on 4.4 gallons of gas.

Correct answer : (1)

9.

For the function, $y$ varies directly as $x$. Find the constant of variation and write the equation.

$x$ | $y$ |

7 | 56 |

9 | 72 |

10 | 80 |

a. | - 8, $y$ = - 8$x$ | ||

b. | $\frac{1}{8}$, $x$ = 8$y$ | ||

c. | 8, $y$ = 8$x$ | ||

d. | - $\frac{1}{8}$, $y$ = ($\frac{1}{8}$)$x$ |

So,

The constant of variation is 8.

The equation is

Correct answer : (3)

10.

For the function, $y$ varies directly as $x$. Find the constant of variation and write the equation.

$x$ | $y$ |

66 | 11 |

42 | 7 |

36 | 6 |

a. | - $\frac{1}{6}$, $y$ = - ($\frac{1}{6}$)$x$ | ||

b. | $\frac{1}{6}$, $x$ = 6$y$ | ||

c. | 6, $y$ = 6$x$ | ||

d. | 6, $x$ = $\frac{1}{6}$$y$ |

So,

Constant of proportionality is

The equation is

Correct answer : (2)