Which of the 2 points (-1,6) or ( -1,5) lie on the line y=-x+4

1 answer

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.

  1. 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.
  2. 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.