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.

Answered by Oliver C. Maths tutor

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