Give the equations of two lines passing through (1, 2). How many more such lines are there and why? 

Two lines passing through (1, 2) are
x + y = 3 ...(1)
and y = 2x ...(2)

Infinitely many more such lines can be found because the general equation of a line is ax + by + c = 0. For a given point (x, y) through which the line passes and for an arbitrary pair of values of a and b, c can be determined so as to satisfy ax + by + c = 0. This holds good for each given point and each arbitrary pair of values of a and b. Hence, infinitely many lines can be found passing through a given point.