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Recognizing Linear Functions

Recognizing Linear Functions 1.6 - Solution

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a

We want to know if the function given in the following table has a constant rate of change.

Time (s), Distance (m),

We can check the rate of change algebraically by noting the change in and change in between each of the data points.

We find the rate of change between each row by dividing the change in by the change in Let's find the rate of change between the first two rows.
The rate of change between the first two rows is approximately In the context of the exercise, this means that the runner ran meters with an average speed of m/s. We can follow the same process for the other given segment splits.
Changes between rows Rate of change

As we can see, the rate of change is not constant. The runner had a higher average speed later in the race than in the middle.

b

We have been asked to find if the function given by the following table has a constant rate of change.

Time (s), Floor number,

Let's find the change in and change in between each of the rows.

We can find the rate of change between each set of points by using the following relationship. We will now find the rate of change for the first two points.
The rate of change between the first two points is Let's repeat this process for the other points.
Changes between rows Rate of change

As we can see, the rate of change is constant. It tells us that the elevator's speed is floors/second.