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.

Line 1 : y = 3x -2. Equation of a line general formula : y = mx + c , where m = gradient. Therefore, for y = 3x - 2, m = 3 and therefore the gradient = 3. Line 2 : 3y - 9x + 5 = 0. Need to get into the general line formula y = mx + c. We can do this by adding 9x to both sides. This gives 3y + 5 = 9x. We can then take 5 from both sides to give 3y = 9x - 5. We can then divide this by 3 to give y = 3x - 5/3. Using y = mx + c, we can see that m = 3 and therefore the gradient = 3. Both lines have a gradient of 3.Lines that have the same gradient are parallel.