To compare the rates of change of the two linear functions, we need to analyze the slope of each function.
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Linear Function 1:
- The equation is given as \( y = 15x + 8 \).
- The slope (rate of change) is 15.
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Linear Function 2:
- We don't have the equation but have the data from a table of points.
- Given points:
- For \( x = 5 \), \( y = 26 \)
- For \( x = 13 \), \( y = 34 \)
- To find the rate of change, we use the formula for slope: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
- Here, \( (x_1, y_1) = (5, 26) \) and \( (x_2, y_2) = (13, 34) \): \[ \text{slope} = \frac{34 - 26}{13 - 5} = \frac{8}{8} = 1 \]
Now we have:
- Linear Function 1: Rate of change = 15
- Linear Function 2: Rate of change = 1
Comparison:
- Linear Function 1 has a greater rate of change (15) compared to Linear Function 2 (1).
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.