Find the constant of variation from a table

Determine the constant of variation.

Miles, x |
Gallons, y |

25 |
1 |

50 |
2 |

75 |
3 |

100 |
4 |

Compare the ratios to check for a
common ratio.

Since the ratios are the same, the function is a direct variation. The
constant of variation is

The table shows the number of hours a clerk works per week and the amount of money she earns before taxes.

Hours worked |
Dollars earned |

13 |
130 |

15 |
150 |

17 |
170 |

19 |
190 |

The relationship between the number of hours she works and the amount of money she earns is linear.

Determine the constant of variation.

Solution: