To determine which set of points lies on the line represented by the equation \( y + 2 = 13(x - 12) \), we first need to convert this equation into a more standard form, such as slope-intercept form.
Starting with the given equation:
\[ y + 2 = 13(x - 12) \]
Distributing \(13\) on the right side:
\[ y + 2 = 13x - 156 \]
Subtracting \(2\) from both sides gives us:
\[ y = 13x - 158 \]
Now we can use this equation to check each set of points. We'll plug in the \(x\) value of each point into the equation to find the corresponding \(y\) value and then see if it matches the original point.
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Check (12, -2) and (15, -1)
- For (12, -2): \[ y = 13(12) - 158 = 156 - 158 = -2 \quad \text{(matches)} \]
- For (15, -1): \[ y = 13(15) - 158 = 195 - 158 = 37 \quad \text{(does not match)} \]
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Check (−12, 2) and (−9, 3)
- For (-12, 2): \[ y = 13(-12) - 158 = -156 - 158 = -314 \quad \text{(does not match)} \]
- For (-9, 3): \[ y = 13(-9) - 158 = -117 - 158 = -275 \quad \text{(does not match)} \]
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Check (−12, 2) and (−11, 3)
- For (-12, 2): \[ y = 13(-12) - 158 = -314 \quad \text{(does not match)} \]
- For (-11, 3): \[ y = 13(-11) - 158 = -143 - 158 = -301 \quad \text{(does not match)} \]
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Check (12, −2) and (13, 1)
- For (12, -2): \[ y = 13(12) - 158 = -2 \quad \text{(matches)} \]
- For (13, 1): \[ y = 13(13) - 158 = 169 - 158 = 11 \quad \text{(does not match)} \]
Now reviewing the results:
- (12, -2) matches for points in the first and fourth set.
- None of the second and third sets have matching points.
Conclusively, only (12, -2) is common between the responses checked for being correct, but the first response is the only pair that includes a point which lies on the line.
Final Answer: The first response (12, -2) and (15, -1) has one correct point.