What is the equation of the line that is perpendicular to the given line and passes through the point (3, 4)? y = –x + 5 y = –x + 3 y = 3x + 2 y = 3x − 5

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First find the slope of the reference line. slope=m=(y2-y1)/(x2-x1)  for any two points (x,y) In this case we have points (-3,2) and (0,1) clearly marked. m=(1-2)/(0--3) m=-1/3 For two lines to be perpendicular their slopes must be negative reciprocals of one another, mathematically: m1*m2=-1, in this case our reference line has a slope of -1/3 so our perpendicular line must have a slope that satisifies: -m/3=-1 m/3=1 m=3, so in the slope-intercept form of a line, y=mx+b, we so far have: y=3x+b, using any point we can now solve for b, the y-intercept (the value of y when x=0), We are told that we must pass through the point (3,4) so: 4=3(3)+b 4=9+b -5=b, now we know the complete equation of the perpendicular line passing through (3,4) is: y=3x-5

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