Are the following lines parallel, perpendicular or neither?

label Mathematics
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schedule 1 Day
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y=1/4x+7

8x-2y=8

May 5th, 2015

The equation of the first line tells us that the slope is 1/4 because the number in front of the x variable represents the slope according to the slope intercept formula y = mx + b.

For the second equation we have to rearrange it into the slope intercept form:

-2y = -8x + 8

y = 4x - 4   The slope here is 4

In order for two lines to be parallel they must have the same slope, therefore these lines are not parallel

In order for two lines to be perpendicular their slopes must be negative reciprocals of each other, but in this case 4 is not the negative reciprocal of 1/4,  it is only the reciprocal. So these lines are not perpendicular.

Therefore the answer is neither.

May 5th, 2015

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