Give the equation of two lines passing through (2,-3). How many more such lines are there and why?

Equation of lines passing through the point (2, -3) are:

x + y = -1  ; 2x + y = 1 etc...

Infinite number of lines pass through a given point. This is because for a unique equation of line, we must have 2 conditions. When only 1 condition is given, we can have infinite number of lines.