Answer:
y = -3x -4
Step-by-step explanation:
A perpendicular line has a slope that is the negative reciprocal of that of the given line. When the equation starts out in standard form, a line with negative reciprocal slope can be written by swapping the x- and y-coefficients and negating one of them.
The given x- and y-coefficients have the ratio 1:-3, so we can use the coefficients 3 and 1 for our purpose.
The usual process of making the line go through a given point can be used. That is, we can translate the line from the origin to the desired point by subtracting the point coordinates from x and y. Then we have ...
3(x+3) +(y-5) = 0
__
This is "an" equation. It is in no particularly recognizable form. It can be rearranged to the form y = mx + b:
3x +9 +y -5 = 0 . . . . . eliminate parentheses
y = -3x -4 . . . . . subtract terms that are not "y"
