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

Two lines are parallel if they have the same gradient. The general equation for a straight line is y=mx+c, where m is the gradient and c is the y-intercept. If these lines are parallel, then m will be the same number for both equations. At the moment, L1 is in the correct y=mx+c form, but L2 needs rearranging into this form.L2: 3y-9x+5=0. Start by taking 5 off each side which gives 3y-9x=-5 and then add 9x to both sides which gives us 3y=9x-5. The straight line general equation needs to start with y=, so we need to divide each side of the equation by 3. This gives us y=3x-5/3. When compared to L1, we can see that in both equations, m = 3, therefore we can concur that these lines are parallel because they have the same gradient.