Find the value of c such that the three points (5,5), (3,1), and \((16,c)\) lie on the same line.
Note: Three points are on the same line if the slope of the line through any two points is always the same.
+2666 The slope of the line is 2.
The point \((16,c)\) is 11 units away from \((5,5)\)
Because the slope is 2, the line goes up 22 from 5, meaning \(c = 5+22=\color{brown}\boxed{27}\)
