# Lesson 4

Comparing Relationships with Tables

Let’s explore how proportional relationships are different from other relationships.

### Problem 1

Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would the constant of proportionality be?

- How loud a sound is depending on how far away you are.
distance to

listener (ft)sound

level (dB)5 85 10 79 20 73 40 67 - The cost of fountain drinks at Hot Dog Hut.
volume

(fluid ounces)cost

($)16 $1.49 20 $1.59 30 $1.89

### Problem 2

A taxi service charges $1.00 for the first \(\frac{1}{10}\) mile then $0.10 for each additional \(\frac{1}{10}\) mile after that.

Fill in the table with the missing information then determine if this relationship between distance traveled and price of the trip is a proportional relationship.

distance traveled (mi) | price (dollars) |
---|---|

\(\frac{9}{10}\) | |

2 | |

\(3\frac{1}{10}\) | |

10 |

### Problem 3

A rabbit and turtle are in a race. Is the relationship between distance traveled and time proportional for either one? If so, write an equation that represents the relationship.

Turtle’s run:

distance (meters) | time (minutes) |
---|---|

108 | 2 |

405 | 7.5 |

540 | 10 |

1,768.5 | 32.75 |

Rabbit’s run:

distance (meters) | time (minutes) |
---|---|

800 | 1 |

900 | 5 |

1,107.5 | 20 |

1,524 | 32.5 |

### Problem 4

For each table, answer: What is the constant of proportionality?

a | b |
---|---|

2 | 14 |

5 | 35 |

9 | 63 |

\(\frac13\) | \(\frac73\) |

a | b |
---|---|

3 | 360 |

5 | 600 |

8 | 960 |

12 | 1440 |

a | b |
---|---|

75 | 3 |

200 | 8 |

1525 | 61 |

10 | 0.4 |

a | b |
---|---|

4 | 10 |

6 | 15 |

22 | 55 |

3 | \(7\frac12\) |

### Problem 5

Here is a table that shows the ratio of flour to water in an art paste. Complete the table with values in equivalent ratios.

cups of flour | cups of water |
---|---|

1 | \(\frac12\) |

4 | |

3 | |

\(\frac12\) |