To determine which of the points \((-1, 6)\) or \((-1, 5)\) lies on the line defined by the equation \(y = -x + 4\), we can substitute the x-coordinates of each point into the equation and see if the resulting y-coordinate matches the y-coordinate of the point.
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For the point \((-1, 6)\):
- Substitute \(x = -1\) into the equation: \[ y = -(-1) + 4 = 1 + 4 = 5 \]
- The calculated \(y\)-value is \(5\), but the point has a \(y\)-coordinate of \(6\). Therefore, \((-1, 6)\) does not lie on the line.
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For the point \((-1, 5)\):
- Substitute \(x = -1\) into the equation: \[ y = -(-1) + 4 = 1 + 4 = 5 \]
- The calculated \(y\)-value is \(5\), which matches the \(y\)-coordinate of the point. Thus, \((-1, 5)\) lies on the line.
In conclusion, the point \((-1, 5)\) lies on the line \(y = -x + 4\), whereas \((-1, 6)\) does not.