To compare the rates of change of the two linear functions, we first identify the slope (rate of change) of each function.
Linear Function 1 is given in slope-intercept form: \[ y = 15x + 8 \] The slope (rate of change) here is 15.
Linear Function 2 is represented by points (5, 26) and (13, 34). We can calculate the slope using the formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Let \( (x_1, y_1) = (5, 26) \) and \( (x_2, y_2) = (13, 34) \): \[ \text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
Now we can summarize the rates of change:
- Linear Function 1: Rate of change = 15
- Linear Function 2: Rate of change = 1
Comparing the two:
- Linear Function 1 has a greater rate of change (15) compared to Linear Function 2 (1).
Therefore, 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.