To compare the rates of change of the two linear functions, we first need to identify the rates of change for each function.
Linear Function 1:
The equation is \( y = 15x + 8 \).
The rate of change (slope) for this function is 15.
Linear Function 2:
To find the rate of change, we can calculate the slope using two points from the provided table:
- Point 1: (5, 26)
- Point 2: (13, 34)
The formula for the slope (rate of change) is given by: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the values:
- \( y_1 = 26 \), \( y_2 = 34 \)
- \( x_1 = 5 \), \( x_2 = 13 \)
\[ \text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
So, the rate of change for Linear Function 2 is 1.
Comparison:
- Rate of change for Linear Function 1: 15
- Rate of change for Linear Function 2: 1
Since \( 15 > 1 \), we conclude that:
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.
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