The equation of the line L1 is: y = 5x-4. The equation for line L2 is 2y-10x+16 = 0. Show that these two lines are parallel.

L1: y=5x-4L2: 2y-10x+16=0. Rearranged: 2y=10x-16, y=5x-8 The coefficient of x is the same in both equations when expressed in standard format (5), therefore the lines are parallel.
Here is how I would talk a student through the question...
[I would first check understanding of what parallel means]It is easiest to think of these lines as being on a graph. When we draw lines on graphs, we like to write their equation in a certain way - a standard way. This format is often called "y = mx + c", or "the standard format". When lines are described like this, the "m" represents the gradient of the line, and the "c" represents how much the line is shifted up or down on the graph (or, the y-intercept) [At this point I would clarify understanding and familiarity - if the student was not too confident with the standard format I would demonstrate it on a graph with a sample line].If two lines are parallel, their gradients must be the same [clarify with graph if necessary]. So we need to rearrange the lines L1 and L2 into this standard format to see if their gradients are the same. If they are, they must be parallel. We can see that the line L1 is already in this format. But we need to rearrange the equation for the line L2 to fit this standard format. [Talk through this with the student, and proceed to rearrange the equation]. Look, when the L2 equation is rearranged into the standard format, the number before x (its coefficient, the "m" value) is the same! Therefore the lines must be parallel. [Draw both lines on graph if student is unsure].