To determine which linear function has the greater rate of change, we first need to analyze both functions.
Linear Function 1:
The equation given is \( y = 15x + 8 \).
The rate of change (slope) for this function is 15.
Linear Function 2:
To find the rate of change for Linear Function 2 from the given points, we can use the formula for the slope, which is:
\[ \text{slope (m)} = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (5, 26) and (13, 34):
- \( (x_1, y_1) = (5, 26) \)
- \( (x_2, y_2) = (13, 34) \)
Now, plugging in these values:
\[ m = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
So, the rate of change for Linear Function 2 is 1.
Comparison:
- The rate of change for Linear Function 1 is 15.
- The rate of change for Linear Function 2 is 1.
Thus, 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.
Therefore, 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.