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Determine if the following lines are parallel (never intersect), perpendicular (intersect at a 90 degree angle), intersecting (intersect at just one point), or coinciding (intersect at all points)?

y = -6x − 8, -x + 6y = 12

Determine if the following lines are parallel (never intersect), perpendicular (intersect-example-1

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Answer:


These lines are perpendicular.

Explanation:

Put both equations in the slope intercept form of a line.

y = -6x - 8 This is already in the slope intercept form for a line

-x + 6y = 12 Add x to both sides of the equation

6y = x + 12 Divide through the whole equation by 6

y = 1/6x +2

Now we compare the two slopes of -6 and 1/6. They are negative reciprocals of each other. That means that the line are perpendicular.

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