2. Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?

Let equation of a line be x + y + c = 0. If (2, 14) lies on it, then 2 + 14 + c = 0 => c = - 16 :. Equation' of a line is % + y - 16 = 0. Let equation of another line be % - 3y + c = 0. If (2, 14) lies on it, then 2 - 42 + c = 0 => c = 40. :. Equation of another line is z - 3y + 40 = 0. There can be infinitely many lines passing through the point (2, 14), because through a point infinitely many lines can be drawn.