To compare the rates of change for Linear Function 1 and Linear Function 2, we will analyze both functions.
Linear Function 1: The equation given is: \[ y = 15x + 8 \] 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: For Linear Function 2, we will calculate the rate of change using the values from the provided table:
| x | y | |----|----| | 5 | 26 | | 13 | 34 |
To find the rate of change (slope), we can use the formula: \[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the coordinates from the table:
- Let \( (x_1, y_1) = (5, 26) \) and \( (x_2, y_2) = (13, 34) \): \[ \text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
So, the rate of change for Linear Function 2 is \( 1 \).
Comparison:
- Rate of change of Linear Function 1 = \( 15 \)
- Rate of change of Linear Function 2 = \( 1 \)
Thus, Linear Function 1 has a greater rate of change than Linear Function 2.
The correct conclusion 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.