Show that the two lines are parallel: L1: 4y = 24x +12, L2: 2y + 13 = 12x

Two lines are parallel when they have the same gradient.
When the equation is written in the form: y = mx + c, m is the gradient.
We need to arrange our equations in the form y = mx + c as this is the easiest way to compare gradients.
L1: 4y = 24x + 12
To get the desired form we need to divide all parts of the equation by 4 giving: y = 6x + 3
L2: 2y + 13 = 12x
Before we do anything we need to rearrange this equation and take 13 over to the other side giving: 2y = 12x - 13Now we can divide it all by 2 to give: y = 6 x - 13/2
Now that we have both equations in the required form we can compare them, as they both have a gradient of 6 we can confirm that they are parallel.