To determine which linear function has the greater rate of change, we can analyze the given equations and values.
Linear Function 1: This function is \( y = 15x + 8 \).
- The rate of change (slope) of a linear function in the form \( y = mx + b \) is given by \( m \).
- Thus, the rate of change for Linear Function 1 is \( 15 \).
Linear Function 2: We need to calculate the rate of change using the provided values.
Given points:
- When \( x = 5 \), \( y = 26 \) (point A: (5, 26))
- When \( x = 13 \), \( y = 34 \) (point B: (13, 34))
The rate of change (slope) between two points is calculated using the formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points: \[ \text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
Now we can compare the rates of change:
- Linear Function 1: rate of change = 15
- Linear Function 2: rate of change = 1
From the calculations:
- 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.