To compare the rates of change of the two linear functions, we can analyze the slope of each function.
Linear Function 1:
The equation for Linear Function 1 is given as \( y = 15x + 8 \). In this linear equation, the coefficient of \( x \) (which is 15) represents the slope. Therefore, the rate of change for Linear Function 1 is 15.
Linear Function 2:
To determine the slope of Linear Function 2, which is presented in tabular form, we can choose any two points from the table. The two points given are \( (5, 26) \) and \( (13, 34) \).
To calculate the slope \( m \), we use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the provided points:
- Let \( (x_1, y_1) = (5, 26) \) and \( (x_2, y_2) = (13, 34) \).
Calculating the slope: \[ m = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
Now we have:
- The rate of change (slope) of Linear Function 1 is 15.
- The rate of change (slope) of Linear Function 2 is 1.
Comparison of Rates of Change:
Since 15 (the rate of change for Linear Function 1) is greater than 1 (the rate of change for Linear Function 2), Linear Function 1 has the greater rate of change.