The equation of line L1 is y=5x-2. The equation of line L2 is 4y-20x=6. Show that these two lines are parallel.

Let's start by recalling that two lines are parallel when their gradients are equal. We know that the gradient of the line y=mx+c, is m. So the gradient of L1 is 5 as the equation of the line is already in the form y=mx+c. We now need to rearrange the equation of L2 to also be in this form. We start by adding 20x to both sides, now we have 4y=20x+6. We then divide the whole equation by 4, this gives y=5x+3/2. We can see that gradient of L2 is also 5. It doesn't matter that the c is different for the two lines, all this is does is shift the line up and down, not affecting the gradient. So the two lines are parallel.