To determine which point lies on the line described by the equation \( Y - 4 = -2(x - 6) \), we can start by rewriting the equation in slope-intercept form ( \( Y = mx + b \) ).
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Start with the given equation: \[ Y - 4 = -2(x - 6) \]
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Distribute on the right side: \[ Y - 4 = -2x + 12 \]
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Add 4 to both sides to solve for \( Y \): \[ Y = -2x + 16 \]
Now we have the equation of the line in slope-intercept form: \( Y = -2x + 16 \).
Next, we'll substitute each of the given points into the equation to see if they satisfy it.
Option A: (4, 6) \[ Y = -2(4) + 16 = -8 + 16 = 8 \quad \text{(not 6)} \]
Option B: (6, 4) \[ Y = -2(6) + 16 = -12 + 16 = 4 \quad \text{(correct)} \]
Option C: (-4, -6) \[ Y = -2(-4) + 16 = 8 + 16 = 24 \quad \text{(not -6)} \]
Option D: (-6, -4) \[ Y = -2(-6) + 16 = 12 + 16 = 28 \quad \text{(not -4)} \]
The only point that satisfies the equation is B. (6, 4).