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We want to find the rate of change for the linear function described by the following data set.

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

$10$ | $6$ |

$20$ | $8$ |

$30$ | $10$ |

$40$ | $12$ |

Let's determine the change in $x$ and the change in $y$ between each data point.

We find the rate of change by using the following relationship. $rate of change=change inxchange iny $ By using the first two rows we can determine the rate of change for the linear function.$rate of change=change inxchange iny $

$rate of change=102 $

ReduceFrac$ba =b/2a/2 $

$rate of change=51 $

b

To determine the rate of change in the given table, we will first determine the change in $x$ and the change in $y$ between each row.

The rate of change is defined as the change in $y$ over the change in $x.$ $rate of change=change inxchange iny $ Let's use the change in $x$ and the change in $y$ between the first and the second row in the table to find the rate of change. We can conclude that the linear function has a rate of change of $-8.$