Question

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

Answer 1

The second and third lines are perpendicular

Explanation:

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).