Is #3x + 4y = 0 # a direct variation equation and if so, what is the constant of variation?

1 Answer
Dec 18, 2015

#3x+4y=0# is a direct variance equation
and its constant of variation is #(-3/4)#

Explanation:

A direct variance function will either be in or can be manipulated to be in the form:
#color(white)("XXX")y=m*x# for some constant #m#, the"constant of variation"

#3x+4y=0#

#rarr 4y=-3x#

#rarr y = (-3/4)x#

Another way to look at it:
If the equation is a straight line which is
#color(white)("XXX")#neither vertical nor horizontal
and
#color(white)("XXX")#passes through the origin #(0,0)#
then it is a direct variation.

Graph of #3x+4y=0#
graph{3x+4y=0 [-10, 10, -5, 5]}