How do you write the equation $- x + 3 y = 7$ $-x+3y=7$ in polar form?

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Answer 1 · 2016-11-12T22:21:24

Please see the explanation

Substitute $r cos (θ)$ $rcos(theta)$ or x and $r sin (θ)$ $rsin(theta)$ for y:

$- r cos (θ) + 3 r sin (θ)$ $-rcos(theta) + 3rsin(theta)$ = 7

Move the common factor r outside ()s:

$r (3 sin (θ) - cos (θ)) = 7$ $r(3sin(theta) - cos(theta)) = 7$

Divide both sides by $(3 sin (θ) - cos (θ))$ $(3sin(theta) - cos(theta))$

$r = \frac{7}{3 sin (θ) - cos (θ)}$ $r = 7/(3sin(theta) - cos(theta))$

Here is a polar graph of the above:

![Desmos.com]( useruploads.socratic.org )

How do you write the equation -x+3y=7−x+3y=7-x+3y=7 in polar form?