To compare the rates of change of the two linear functions, we need to analyze them individually.
-
Linear Function 1: \( y = 15x + 8 \)
- The rate of change (slope) of this function is 15.
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Linear Function 2: We need to calculate the rate of change based on the provided table of values.
Given:
- For \( x = 5 \), \( y = 26 \)
- For \( x = 13 \), \( y = 34 \)
To find the rate of change, we can use the formula for slope: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the values from the table: \[ \text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
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.
So, Linear Function 1 has the greater rate of change.
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.