# Lesson Worksheet: Direct Variation Mathematics

In this worksheet, we will practice describing direct variation between two variables and using this to solve word problems.

**Q1: **

A recipe for 4 people requires 440 g of spaghetti. The quantity of spaghetti is proportional to the number of people. What is the corresponding constant of proportionality (unit rate)?

- A110 g/person
- B440 g/person
- C1 760 persons/g
- D1 760 g/person
- E110 persons/g

**Q2: **

One gallon of gas cost $2.75 in October 2017. The graph represents the price of different volumes of gas at that time.

What is the gradient of the graph?

Write an equation for the cost (dollars) of gallons of gas.

- A
- B
- C
- D
- E

**Q3: **

The amount of caffeine in a cup of coffee is roughly 95 mg. What is the constant of proportionality, or unit rate, between the amount of caffeine ingested and the number of cups taken?

**Q4: **

If , where is a constant, then .

- A
- B
- C
- D

**Q5: **

For the following table, find the algebraic equation that shows the proportional relationship between and .

6 | 12 |

7 | 14 |

8 | 16 |

- A
- B
- C
- D
- E

**Q6: **

Dima walks to school every day. Find her speed from the distance-time graph.

**Q7: **

The given table shows the total distance traveled by a bus driving at a constant speed. Using this information, determine how far the bus will have traveled after 10 hours.

Time (h) | Distance (mi) |
---|---|

2 | 142 |

5.7 | 404.7 |

6 | 426 |

7 | 497 |

**Q8: **

Select the graph that shows a proportional relationship.

- A
- B
- C
- D
- E

**Q9: **

If and when , find the value of when .

**Q10: **

If and when , determine the constant of proportionality.

- A14
- B
- C84
- D6
- E