To compare the rates of change for the two linear functions, we start with Linear Function 1 and then find the rate of change for Linear Function 2 from the provided data.
Linear Function 1:
The function is given in slope-intercept form \( y = 15x + 8 \).
- The rate of change (slope) is the coefficient of \( x \), which is 15.
Linear Function 2:
We need to determine the rate of change from the provided table. The table has the following data points:
- When \( x = 5 \), \( y = 26 \)
- When \( x = 13 \), \( y = 34 \)
To find the rate of change (slope), we can use the formula: \[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points \( (5, 26) \) and \( (13, 34) \):
- \( y_1 = 26 \), \( y_2 = 34 \)
- \( x_1 = 5 \), \( x_2 = 13 \)
Now plug in the values: \[ \text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
Summary of Rates of Change:
- Linear Function 1 has a rate of change of 15.
- Linear Function 2 has a rate of change of 1.
Conclusion:
Linear Function 1 has the greater rate of change, which is 15, compared to Linear Function 2’s rate of change of 1.
So the correct response would be: 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.