line P is Y=1/5x+2, line Q is Y=5x-1/2 and line R is -5x+3, Which line is perpendicular. Explain

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Lines are perpendicular to each other when the product of the slopes is -1 (or opposite reciprocals). Because the slope of the line is 1/5 (y=mx +b, where m is the slope), the line perpendicular to it would have a slope of -5. Therefore, line R perpendicular to line P.