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.

We should recall that two lines are parallel when they have the same gradient. We can see the gradient of a line by writing it in the form y=mx+c, which will make the gradient equal to the coefficient of x (the number in front of the x). Our first line is already in the form y=3x-2 so we can see that the gradient is 3. The second line needs rearranging as follows: 3y-9x+5=0 3y=9x-5 (add 9x and minus 5 from each side) y=3x-(5/3) (divide each side by 3). Now we can see that the gradient of this line is also 3. So the two lines must be parallel.