If L1 is y = 3x + 15 and L2 is 3y + 20 = 9x show whether or not L1 and L2 are parallel.

Theory - Two lines on a graph will be parallel if their gradient is the same. The general equation of a line is y = mx + c where y and x are variables, m is the gradient and c is the y intercept. hence if the values of m are the same then the lines will be parallel. This means that the lines will not intersect and when equated will have no solutions.
For this specific example we would want to rearrange L2 into the form of L1, hence we can carry over 20 to the RHS, then divide the whole equation by 3 to give y = 3x - (20/3). If we now compare the two equations the gradient m will be 3 for both L1 and L2.