To compare the rates of change of the two linear functions, we can analyze their slopes.
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Linear Function 1: \( y = 7x + 4 \)
- The slope (rate of change) is 7.
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Linear Function 2: To determine the slope from the given points (10, 6) and (12, 7), we can use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\): \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the values:
- \( (x_1, y_1) = (10, 6) \)
- \( (x_2, y_2) = (12, 7) \) \[ \text{slope} = \frac{7 - 6}{12 - 10} = \frac{1}{2} = 0.5 \]
Now we can compare the slopes:
- Slope of Linear Function 1: 7
- Slope of Linear Function 2: 0.5
Since 0.5 is less than 7, Linear Function 2 has the lesser rate of change.
Final answer: 2 (Linear Function 2 has the lesser rate of change).