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

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

Multiplication property of zero