Average rate of change is the change in the function per unit in a given interval. The average rate of change from [tex]x = 5[/tex] to [tex]x = 7[/tex] is -4
Given
The graph of [tex]y = f(x)[/tex]
See attachment for the points on f(x) that links [tex]x = 5[/tex] to [tex]x = 7[/tex]
The line segment is represented by a green line
To determine the average rate of change using the line segment; we have the following values.
When [tex]x =5; y = 8[/tex]
When [tex]x =7; y = 0[/tex]
So, the average rate of change (m) is:
[tex]m = \frac{\Delta y}{\Delta x}[/tex]
Where:
[tex]\Delta y = y_2 - y_1[/tex]
[tex]\Delta y = 0-8[/tex]
[tex]\Delta y = -8[/tex]
[tex]\Delta x = x_2 - x_1[/tex]
[tex]\Delta x = 7 - 5[/tex]
[tex]\Delta x = 2[/tex]
So, we have:
[tex]m = \frac{\Delta y}{\Delta x}[/tex]
[tex]m = \frac{-8}{2}[/tex]
[tex]m = -4[/tex]
Hence, the average rate of change from [tex]x = 5[/tex] to [tex]x = 7[/tex] is -4
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