To determine if the points (0,6), (3,3), and (6,-1) are on the same line, you can calculate the slope between each pair of points. If the slopes are the same, then the points are collinear (on the same line).
Let's calculate the slopes between these points:
Slope between (0,6) and (3,3):
Slope = (y2 - y1) / (x2 - x1)
Slope = (3 - 6) / (3 - 0)
Slope = (-3) / (3)
Slope = -1
Slope between (3,3) and (6,-1):
Slope = (y2 - y1) / (x2 - x1)
Slope = (-1 - 3) / (6 - 3)
Slope = (-4) / (3)
Slope = -4/3
The slopes between the points are not the same. The first slope is -1, and the second slope is -4/3. Therefore, these points are not collinear and do not lie on the same line.