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True or False: Two non-vertical lines are perpendicular if and only if they have negative reciprocal slopes.

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Final answer:

Two non-vertical lines are perpendicular if their slopes are negative reciprocals, reflecting a true inverse proportionality that causes them to intersect at a 90° angle.

Step-by-step explanation:

The statement is True: Two non-vertical lines are perpendicular if and only if they have negative reciprocal slopes. To be perpendicular means that two lines intersect to form a 90° angle. When the slopes of two lines are negative reciprocals of each other, it means that one slope is the negative inverse of the other. For example, if one line has a slope of 2, a line perpendicular to it would have a slope of -1/2. A negative slope indicates that as the value of x increases, the value of y decreases, and vice versa. This negative relationship conveys that the two lines inversely proportional to each other, and when graphed, they would intersect to form right angles.

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