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.

First of all, you are trying to prove that these two lines are parallel. So how would we be able to show this… Well two lines are parallel to one another if they have the same gradient (draw demonstration). The equation of a line can be represented by y=mx+c where m is the gradient and c is the y intercept (where the line crosses the y axis). So, we need to show that L1 and L2 have the same gradient (m in our equation).L1 equation is already in our original format, so I would suggest manipulating the equation for L2 so we have y=something. So, -5 to both sides of the = sign means that we have 3y-9x=-5, then +9x to both sides so we are left with 3y=9x-5. Now as we said before we want y=something, so this means we need to divide by 3 to both sides. This makes our equation of L2: y=3x-5/3. As both L1 and L2 have the same gradient of 3 then this shows they are parallel.