The equation of the line L1 is y=3x–2. The equation of the line L2 is 3y–9x+5=0. Show that these two lines are parallel.

The first thing that you should know when wanting to find out if two lines are parallel are the features of a parallel line. These key features include never intersecting lines which means they continue forever without touching and identical slopes also called gradients which means the change in y over the change in x for both lines are the same. Once you remember the key features, you will look at both equations and see that the equation of the line L1 is in a different format to the equation of line 2, so to make it easier to decide whether the lines are parallel, you will need to get them both into the same format. Therefore, you will rearrange the equation of line L2 by taking the gradient and the y intercept onto the other side of the equal sign and you will get 3y = 9x - 5. Now, to get the y on its own you will need to divide both sides by 3 and you will get y = 3x - 5/9. Now that you have both equations in the same format you can see that they both have the same slope of 3x and therefore you can conclude that these two lines are parallel.