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Are the lines #y=8x-5, y=1/8x+1# and #8x+y=2# parallel or perpendicular?

Answer 1

Allison Allen

The second and third lines are perpendicular

If you restructure the third equation by subtracting #8x# from both sides, you'll get

#y=-8x+2#

With

#y=mx+b" "# [here #m = #slope]

you know the slope of all three lines: #8#, #1/8#, and #-8#, respectively.

Two lines are perpendicular when their slopes are negative reciprocals . You can see that two slopes are negative reciprocals if #-1# divided by one slope equals the other slope.

Because #-1# divided by #-8# equals #1/8#, you know that the second and third equations have negative reciprocal slopes, therefore they are perpendicular.

The first equation isn't perpendicular to either of the other two lines because #-1# divided by #8# is #-1/8#, which does not match any of the other slopes. It isn't parallel either (parallel lines have the same slope).

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Answer 2

Aaliyah Anderson

The lines ( y = 8x - 5 ) and ( y = \frac{1}{8}x + 1 ) are perpendicular.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.