The slope of a line perpendicular to a line with slope m is what?

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Multiple Choice

The slope of a line perpendicular to a line with slope m is what?

When two lines are perpendicular, their slopes are negatives reciprocals of each other. So if a line has slope m, the line perpendicular to it must have slope -1/m (as long as m is not zero). This is because m times -1/m equals -1, which is the defining relationship for perpendicular slopes. For intuition, try a quick example: if m = 2, the perpendicular slope is -1/2; if m = -3, it becomes 1/3. Special cases: if the original line is horizontal (m = 0), the perpendicular line is vertical (undefined slope). If the original is vertical (undefined slope), the perpendicular line has slope 0 (horizontal). That negative reciprocal is why the correct choice is -1/m. Using m would give a parallel line, using -m would not make the lines perpendicular, and using 1/m would be the reciprocal but not the negative.

When two lines are perpendicular, their slopes are negatives reciprocals of each other. So if a line has slope m, the line perpendicular to it must have slope -1/m (as long as m is not zero). This is because m times -1/m equals -1, which is the defining relationship for perpendicular slopes. For intuition, try a quick example: if m = 2, the perpendicular slope is -1/2; if m = -3, it becomes 1/3.

Special cases: if the original line is horizontal (m = 0), the perpendicular line is vertical (undefined slope). If the original is vertical (undefined slope), the perpendicular line has slope 0 (horizontal).

That negative reciprocal is why the correct choice is -1/m. Using m would give a parallel line, using -m would not make the lines perpendicular, and using 1/m would be the reciprocal but not the negative.

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