The equation of line L1 is y=4x+3, The equation of line L2 is 4y-16x-2=0, Show that these two lines are parallel.

The equation of a line is shown in the form y=mx+c to prove that two lines run parallel you must prove that they have the same gradient or value of 'm', the number before x. The first equation L1 is already in the y=mx+c form meaning 4 is the 'm' value or the gradient. To show the other equation L2 has the same gradient you need to rearrange it. 4y-16x-2=0, 16x-2 can be added to both sides making 4y=16x+2, the whole equation can then be divided by 4 making y=4x+1/2. You can then see that the gradient or the 'm' value of this equation is 4.Both equations have a gradient of 4, proving that the two lines L1 and L2 are parallel.