To determine which set of points lies on the line represented by the equation \(y + 2 = 13(x - 12)\), we can first rewrite the equation in slope-intercept form (y = mx + b).
Starting with the given equation:
\[ y + 2 = 13(x - 12) \]
Expanding the right side:
\[ y + 2 = 13x - 156 \]
Now, solving for \(y\):
\[ y = 13x - 158 \]
This is the equation of the line in slope-intercept form.
Now we can test each of the provided points to see if they satisfy the equation \(y = 13x - 158\).
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Testing the points \((-12, 2)\) and \((-9, 3)\):
- For \((-12, 2)\): \[ 2 = 13(-12) - 158 \implies 2 = -156 - 158 \implies 2 = -314 \quad \text{(Not on the line)} \]
- For \((-9, 3)\): \[ 3 = 13(-9) - 158 \implies 3 = -117 - 158 \implies 3 = -275 \quad \text{(Not on the line)} \]
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Testing the points \((12, -2)\) and \((13, 1)\):
- For \((12, -2)\): \[ -2 = 13(12) - 158 \implies -2 = 156 - 158 \implies -2 = -2 \quad \text{(On the line)} \]
- For \((13, 1)\): \[ 1 = 13(13) - 158 \implies 1 = 169 - 158 \implies 1 = 11 \quad \text{(Not on the line)} \]
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Testing the points \((12, -2)\) and \((15, -1)\):
- For \((12, -2)\): We've already determined this is on the line.
- For \((15, -1)\): \[ -1 = 13(15) - 158 \implies -1 = 195 - 158 \implies -1 = 37 \quad \text{(Not on the line)} \]
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Testing the points \((-12, 2)\) and \((-11, 3)\):
- We have already tested \((-12, 2)\) and found it is not on the line.
- For \((-11, 3)\): \[ 3 = 13(-11) - 158 \implies 3 = -143 - 158 \implies 3 = -301 \quad \text{(Not on the line)} \]
After evaluating all the points, the only point we found that lies on the line is \((12, -2)\), but the other points tested with it do not satisfy the equation. Therefore, none of the provided pairs have both points on the line.
The conclusion is that the only point that lies on the line is \((12, -2)\).
However, since no complete pair was found to lie on the line and there's no indication specifying whether a single point is enough, none of the specified point pairs lie entirely on the line.