Recognizing Linear Functions

a

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

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 = \frac{change in y}{change in x}

By using the first two rows we can determine the rate of change for the linear function.

rate of change = \frac{change in y}{change in x}

change in x = 10

,

change in y = 2

rate of change = \frac{2}{1 0}

\frac{a}{b} = \frac{a / 2}{b / 2}

rate of change = \frac{1}{5}

Thus, the linear function has a rate of change of

\frac{1}{5} .

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 = \frac{change in y}{change in x}

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.

rate of change = \frac{change in y}{change in x}

change in x = 1

,

change in y = - 8

rate of change = \frac{- 8}{1}

\frac{a}{1} = a

rate of change = - 8

We can conclude that the linear function has a rate of change of

- 8 .

Recognizing Linear Functions 1.2 - Solution