To compare the rates of change of the two given linear functions, we first look at their forms.
Linear Function 1: \[ y = 15x + 8 \]
- The rate of change (slope) for this function is 15.
Linear Function 2: The data for Linear Function 2 is given in the form of points: (5, 26), (13, 34). To find the rate of change, we can calculate the slope using the slope formula, which is \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points:
- \( (x_1, y_1) = (5, 26) \)
- \( (x_2, y_2) = (13, 34) \)
Now, applying the values: \[ m = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
So the rate of change (slope) for Linear Function 2 is 1.
Comparison:
- The rate of change for Linear Function 1 is 15
- The rate of change for Linear Function 2 is 1
Thus, Linear Function 1 has the greater rate of change.
Final Answer: Linear Function 1 has the greater rate of change, with a rate of change equal to 15 while Linear Function 2 has a rate of change equal to 1.
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