How do I find the equation of a line connecting points a(p,q) and b(r,s)?

First we need to find the gradient of the line connecting points a and b:
gradient m = (change in y)/(change in x) = (q - s)/(p -r)

Now we use the following equation:

y - y1 = m(x - x1)

substituting suitable values for (x1, y1) (can be points a or b but we'll use point a this time) and m (calculated above):

Using point a:

y - q = [(q-s)/(p-r)](x - p)

and so the equation in the form y = f(x) is:
y = [(q-s)/(p-r)]x + (q-s)/(p-r) + q