To find a point on the line represented by the equation \(y - 5.5 = \frac{4}{1}(x + 2)\), we need to simplify the equation and find points that satisfy it.
First, simplify the equation:
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Start with the given equation: \[ y - 5.5 = 4(x + 2) \]
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Distribute the 4: \[ y - 5.5 = 4x + 8 \]
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Add 5.5 to both sides to solve for \(y\): \[ y = 4x + 8 + 5.5 \] \[ y = 4x + 13.5 \]
Now we have the equation of the line in slope-intercept form \(y = mx + b\), where \(m = 4\) and \(b = 13.5\).
Next, we can check which of the provided points lies on this line.
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Point (-2, 5.5): \[ y = 4(-2) + 13.5 = -8 + 13.5 = 5.5 \quad \text{(True)} \]
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Point (2, -5.5): \[ y = 4(2) + 13.5 = 8 + 13.5 = 21.5 \quad \text{(False)} \]
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Point (5.5, -2): \[ y = 4(5.5) + 13.5 = 22 + 13.5 = 35.5 \quad \text{(False)} \]
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Point (-5.5, 2): \[ y = 4(-5.5) + 13.5 = -22 + 13.5 = -8.5 \quad \text{(False)} \]
The only point that satisfies the equation \(y = 4x + 13.5\) is (-2, 5.5).
Thus, the correct answer is (−2, 5.5).