To compare the rates of change for Linear Function 1 and Linear Function 2, let's analyze each function.
Linear Function 1:
The equation is given as: \[ y = 15x + 8 \] In this equation, the coefficient of \( x \) (which is 15) represents the rate of change (slope). Therefore, the rate of change for Linear Function 1 is 15.
Linear Function 2:
A table presents the values for \( x \) and \( y \):
| x | y | |-------|-------| | 5 | 26 | | 13 | 34 |
To find the rate of change for Linear Function 2, we can use the points provided in the table. The formula for the slope (rate of change) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Plugging in the values:
- Let \((x_1, y_1) = (5, 26)\) and \((x_2, y_2) = (13, 34)\).
Calculating the slope: \[ \text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
Summary of Rates of Change:
- Linear Function 1 rate of change: 15
- Linear Function 2 rate of change: 1
Conclusion:
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.
Thus, 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.