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Recognizing Linear Functions

Recognizing Linear Functions 1.3 - Solution

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a

We want to find the rate of change for the linear function in the following diagram.

We can see that the graph passes through the points and Let's mark these points in the diagram.

Let's draw arrows to show what it looks like to move from one point to the other by taking one horizontal step followed by a vertical. The horizontal step we label and the vertical

In the diagram we can see that and By using these values in the relationship we find the rate of change.
Thus, the rate of change for the graphed function is
b

Observing the given graph, we can see that the line passes through the points and We can move from one point to the other by taking one horizontal step, followed by a vertical step,

We can in the graph see that the horizontal step we take is making The vertical step is down units. Moving down makes the step negative. Therefore, We find the rate of change using this relationship. Let's use the values we have found to calculate the rate of change.
We have found that the rate of change for the linear function is