Your friend says that y = 2x - 5 is perpendicular to the line y=1/2x+5 which passes through (2, 6). She proves it with the following work:

These two lines cannot be perpendicular. For one line to be perpendicular to the second one, their gradients are related by the following:

Gradient of line 1 = - (1/gradient of line two)

In the current case, gradient of line 1=2 and gradient of line two = 1/2. If gradient of line two was = - 1/2, then they would be perpendicular.