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Find the slope of the line that is perpendicular to x-y=3

Graph equation and show work step by step

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Our answering system doesn't allow the posting of graphical pictures.  If you want to graph an equation perpendicular to y=x-3, plot two points for any equation that has a slope of -1.  A simple example would be y = -x -3, which would pass through the point (0, -3) just like your original equation..

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1 Answer

A line that is perpendicular will have a slope that is the negative reciprocal of the slope of a given line. For example, if the slope of a line was 3, then the perpendicular line would have slope -1/3

Given x - y = 3, let's get this into slope-intercept form y = mx + b

-y = -x + 3   (now divide by -1)

y = x - 3

So our slope is 1. Therefore, the slope of our perpendicular line is -1/1 = -1