In a xy plane, the equation of a line is #x+3y=12#. What is an equation of a line that is perpendicular to it?

1 Answer
Aug 29, 2016

Answer:

#y=3x+c# (for all #c in RR#)
For example, #y=3x+4#

Explanation:

The equation of a straight line in slope (#m#) and intercept (#c#) form is:

#y = mx+c#

In this example we are given the equation: #x+3y=12#

Rearranging terms:
#3y=-x+12#

#y=-1/3x+4#

Hence: #m=-1/3# and #c=4#

For two straight lines to be perpendicular to eachother their slopes
(#m_1 and m_2#) must satisfy the relationship: #m_1xxm_2 =-1#

Hence the straight lines perpendicular to the line with a slope of #-1/3# will have slopes of #-1/(-1/3) = 3#

#:.# The straight lines perpendicular to the given line will have equations:

#y=3x+c# (for all #c in RR#)

For example, the line perpendicular to the given line with the same intercept is #y=3x+4#