To compare the rates of change of Linear Function 1 and Linear Function 2, let's first identify the rate of change for each function.
Linear Function 1 is given as: \[ y = 15x + 8 \] The coefficient of \( x \) (which is 15) represents the rate of change. Therefore, the rate of change for Linear Function 1 is 15.
Linear Function 2 is represented by the table of \( x \) and \( y \) values:
- For \( x = 5 \), \( y = 26 \)
- For \( x = 13 \), \( y = 34 \)
To find the rate of change (slope) of Linear Function 2, we can use the formula for slope: \[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (5, 26) \) and \( (x_2, y_2) = (13, 34) \).
Calculating the change in \( y \) and \( x \): \[ \Delta y = 34 - 26 = 8 \] \[ \Delta x = 13 - 5 = 8 \]
Now calculate the rate of change: \[ \text{slope} = \frac{8}{8} = 1 \]
Now we can compare the rates of change:
- Linear Function 1 has a rate of change of 15.
- Linear Function 2 has a rate of change of 1.
Thus, Linear Function 1 has a greater rate of change compared to Linear Function 2.
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.