If a line has slope -2, what is the slope of a line perpendicular to it?

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Multiple Choice

If a line has slope -2, what is the slope of a line perpendicular to it?

Perpendicular lines have slopes that are negative reciprocals of each other. So if one line has slope m, a line perpendicular to it has slope -1/m. With m = -2, the perpendicular slope is -1/(-2) = 1/2. Checking the product confirms it: (-2) × (1/2) = -1, which is the condition for perpendicularity. Therefore, the slope 1/2 is the correct perpendicular slope. The other options do not satisfy the -1 product requirement (for example, 2 or -2 would not give -1 when multiplied by -2), so they aren’t perpendicular.

Perpendicular lines have slopes that are negative reciprocals of each other. So if one line has slope m, a line perpendicular to it has slope -1/m. With m = -2, the perpendicular slope is -1/(-2) = 1/2. Checking the product confirms it: (-2) × (1/2) = -1, which is the condition for perpendicularity. Therefore, the slope 1/2 is the correct perpendicular slope. The other options do not satisfy the -1 product requirement (for example, 2 or -2 would not give -1 when multiplied by -2), so they aren’t perpendicular.

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