To compare the rates of change of Linear Function 1 and Linear Function 2, we need to determine the slope (rate of change) for each.
Linear Function 1 is given as: \[ y = 15x + 8 \] The coefficient of \( x \) (which is 15) represents the rate of change for this linear function. Thus, the rate of change for Linear Function 1 is 15.
Linear Function 2 can be determined from the points provided:
- When \( x = 5, y = 26 \)
- When \( x = 13, y = 34 \)
To find the rate of change (slope) of Linear Function 2, we can use the formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (5, 26) and (13, 34): \[ \text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
So, the rate of change for Linear Function 2 is 1.
Now comparing the two rates of change:
- Linear Function 1: 15
- Linear Function 2: 1
Thus, 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.
The correct response is: 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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