To compare the rates of change of the two linear functions, we need to identify the rate of change, which is represented by the coefficient of \(x\) in the equation of a linear function or can be calculated using points for a function given in a table.
Linear Function 1:
The function is given as: \[ y = 15x + 8 \] Here, the coefficient of \(x\) is \(15\). Therefore, the rate of change for Linear Function 1 is \(15\).
Linear Function 2:
We have two points:
- \( (5, 26) \)
- \( (13, 34) \)
We can find the rate of change (slope) by using the formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the points:
- \( (x_1, y_1) = (5, 26) \)
- \( (x_2, y_2) = (13, 34) \)
Calculating the slope: \[ \text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
So, the rate of change for Linear Function 2 is \(1\).
Comparison
- Linear Function 1 has a rate of change of \(15\).
- Linear Function 2 has a rate of change of \(1\).
Conclusion
Linear Function 1 has the greater rate of change.
Final 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.