To compare the rates of change (slopes) of Linear Function 1 and Linear Function 2, we can analyze each function:
Linear Function 1: The function is given as \( y = 15x + 8 \). The rate of change (slope) is the coefficient of \( x \), which is \( 15 \).
Linear Function 2: This function is presented as a set of points: (5, 26) and (13, 34). To find the rate of change, we can use the slope formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Plugging in the given points, where \( (x_1, y_1) = (5, 26) \) and \( (x_2, y_2) = (13, 34) \):
\[ \text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
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 \( 1 \).
Therefore, Linear Function 1 has the greater rate of change.
Correct response: 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.