How do you find the equation of a line that Contains point (5, -3) and is perpendicular to y=5x?

1 Answer
Karthik G
Jan 18, 2016

#y=-1/5x -2#

Explanation:

For finding an equation of a perpendicular line, we start with finding the slope of the given line. Slope of the perpendicular line is negative reciprocal of the given slope. For example, if the slope is #m# then the slope of the perpendicular would be #-1/m#

Equation of the form #y=mx+b# has the slope as #m#

Using this knowledge, we can see that the slope of the line #y=5x# is #5#

The slope of the perpendicular line is #-1/5#

We can say our line would be

#y=-1/5x + b#

We need to find #b# to find the equation. This is where the point#(5,-3)# is used.

Let us substitute the value #x=5# and #y=-3# in the equation #y=-1/5x+b#

We get,
#-3=-1/5(5)+b#
#-3=-1+b#
Add #1# to both the sides.

#-3+1=b#

#-2=b#

Our equation becomes #y=-1/5x -2#

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