Linear Relations

Lesson

We've already learnt about rates which are a special type of ratios that are used to compare different types of quantities.

A *unit rate* describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

Some common unit rates are distance per hour, cost per item, earnings per week, etc. Do you see how in each example the first quantity is related to *one* unit of the second quantity?

When we are looking at unit rates on graphs, we want to know how much the dependent ($y$`y`) variable will increase by when the independent ($x$`x`) variable is increased by one.

Consider this table:

$x$x |
$y$y |
---|---|

$1$1 | $6$6 |

$2$2 | $12$12 |

$3$3 | $18$18 |

$4$4 | $24$24 |

$5$5 | $30$30 |

Plot the line.

Loading Graph...State the unit rate of the graph you have plotted.

Consider this table:

$x$x |
$y$y |
---|---|

$2$2 | $5$5 |

$3$3 | $7.5$7.5 |

Plot the line.

Loading Graph...State the unit rate of the graph you have plotted.

Determine, through investigation, that the rate of change of a linear relation can be found by choosing any two points on the line that represents the relation, finding the vertical change between the points (i.e., the rise) and the horizontal change between the points (i.e., the run), and writing the ratio