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

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Answer 1 · 2016-06-27T02:38:27

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

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]( useruploads.socratic.org )

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

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