Find the gradient of a straight line with the points P(5,3) and Q(8,12)

First we draw a picture, to visually see what the question is asking. A simple set of coordinate-axes and notches so we can accurately put our point P and Q, though being accurate isn't important it will give a good idea of what kind of numbers we are looking for. Now the gradient represents 'for every step x along, we go y steps up' so we want to divide dy (the differnce in the y values) by dx (the differnce in the x values). That is to say dy/dx=(12-3)/(8-5)=9/3=3. This is the answer.