To compare the rates of change of the two linear functions, let's analyze both functions:
Linear Function 1:
The function 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:
- Rate of Change (Linear Function 1) = 15
Linear Function 2:
To calculate its rate of change, we can use the two points provided: (5, 26) and (13, 34). The rate of change (slope) can be calculated as follows:
\[ \text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
So, the rate of change for Linear Function 2 is:
- Rate of Change (Linear Function 2) = 1
Comparison:
- Rate of Change (Linear Function 1) = 15
- Rate of Change (Linear Function 2) = 1
From this comparison, we can conclude that:
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.
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."