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.

In this question, you are being asked to show L1 and L2 are parallel. The equations of two parallel lines will have the same gradient. This is the number in front of the x term in the equation, but to compare the two equations they have to be in the same form. The equation for L1 is in the form y=mx+c but the equation for L2 is in the form Ay - mx + c =0 which is more complex. So the first thing to do in this question is to rearrange the equation for L2 into the y=mx+c form. Start with:3y – 9x + 5 = 0 - start by putting y term on one side and other terms on the other side 3y = 9x - 5 - next need to change 3y to make it y by dividing both sides by 3y= (9/3)x- (5/3). So y=3x- (5/3) - L2 is now in the same form as L1Comparing the m term of both equations shows they m=3 for both equations, therefore, they are parallel