If a line has slope m, which is the slope of a line perpendicular to it (assuming m ≠ 0)?

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Multiple Choice

If a line has slope m, which is the slope of a line perpendicular to it (assuming m ≠ 0)?

Explanation:
Perpendicular lines have slopes that multiply to -1. So if one line has slope m (and m ≠ 0), the slope of a line perpendicular to it must be the negative reciprocal, which is -1/m. This ensures m times (-1/m) equals -1, regardless of the specific nonzero value of m. If m is positive, the perpendicular slope is negative; if m is negative, it’s positive. The other possibilities don’t satisfy the perpendicularity condition: using m would yield parallel lines, m^2 isn’t related to perpendicular slopes, and 1/m is the reciprocal without the required negative sign.

Perpendicular lines have slopes that multiply to -1. So if one line has slope m (and m ≠ 0), the slope of a line perpendicular to it must be the negative reciprocal, which is -1/m. This ensures m times (-1/m) equals -1, regardless of the specific nonzero value of m. If m is positive, the perpendicular slope is negative; if m is negative, it’s positive. The other possibilities don’t satisfy the perpendicularity condition: using m would yield parallel lines, m^2 isn’t related to perpendicular slopes, and 1/m is the reciprocal without the required negative sign.

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