How do you convert #y=4x-7# into polar form?

1 Answer

#y=4x-7# is equivalent to #color(red)(r=7/(4*cos theta-sin theta))#

Explanation:

We start with the given equation #y=4x-7#

We should know that equivalent of #x#

#x=r cos theta#

We should also know that equivalent of #y#

#y=r sin theta#

#y=4x-7#

#r sin theta=4(r cos theta)-7#

#r sin theta-4*r cos theta=-7#

#r(sin theta-4*cos theta)=-7#

#r=(-7)/(sin theta-4*cos theta)#

#r=7/(4*cos theta-sin theta)#

Kindly see the graph of #r=7/(4*cos theta-sin theta)#

Desmos.com

God bless....I hope the explanation is useful.