What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (2, −1)? y = x − y = x − y = 3x − 3 y = 3x − 7

The equation of the line which is perpendicular to the given lines and cuts through point (2,-1) will be found as follows: a] equation of the line perpendicular to y=3x-3.to get the equation of the perpendicular line we need to find the slope first. to start with, the slope of y=3x-3 which is in the form of y=mx+b where m is the slope is m=3.thus the slope of the perpendicular line will be: m1 such that: -1=m×m1plugging the values that we know in the above equation we get: -1=3×m1thus solving for m1 we get: m1=-1/3hence the slope of the perpendicular line is m1=-1/3the equation of this line will therefore be given by: m1(x-x1)=(y-y1)plugging the values we get: -1/3(x-2)=(y--1)-1/3x+2/3=y+1hencey=-1/3x+2/3-1y=-1/3x-1/3hence the equation of the perpendicular line to y=3x-3 that passes through (2,-1) is y=-1/3x-1/3b] equation of the perpendicular line to y=3x-7 and cuts through point (2,-1).as shown above we will require the slope of the perpendicular line: from-1=m×m1where m=3 is the slope of y=3x-7 and m1 the slope of the perpendicular linethen-1=3×m1where: m1=-1/3hence the equation of the perpendicular line will be: m(x-x1)=y-y1-1/3(x-2)=(y--1)=-1/3x-2/3=y+1thusy=-1/3x-1/3

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