The equation of line L is y= 3x+2 and the equation of line M is 3y–9x+5=0. Show that these lines are parallel.

First step is to understand what it means for lines to be parallel. This is when the gradients of two lines are the same.This is much easier to see when the format of the equations is the same, so lets rearrange line M to the standard y = mx + c format, where m denotes the gradient of the lines.Let's add 9x to both sides of equation M to get: 3y + 5 = 9xNow let's take away 5 both sides: 3y = 9x - 5Divide both sides by 3 so that we have y = 3x - (5/3)On comparing the m values we can see that both have a value of 3, meaning that the lines have the same gradient and will therefore never cross.