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

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Answer 1 · 2016-06-27T02:38:27

$y = 4 x - 7$ $y=4x-7$ is equivalent to $r = \frac{7}{4 \cdot cos θ - sin θ}$ $color(red)(r=7/(4*cos theta-sin theta))$

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

We should know that equivalent of $x$ $x$

$x = r cos θ$ $x=r cos theta$

We should also know that equivalent of $y$ $y$

$y = r sin θ$ $y=r sin theta$

$y = 4 x - 7$ $y=4x-7$

$r sin θ = 4 (r cos θ) - 7$ $r sin theta=4(r cos theta)-7$

$r sin θ - 4 \cdot r cos θ = - 7$ $r sin theta-4*r cos theta=-7$

$r (sin θ - 4 \cdot cos θ) = - 7$ $r(sin theta-4*cos theta)=-7$

$r = \frac{- 7}{sin θ - 4 \cdot cos θ}$ $r=(-7)/(sin theta-4*cos theta)$

$r = \frac{7}{4 \cdot cos θ - sin θ}$ $r=7/(4*cos theta-sin theta)$

Kindly see the graph of $r = \frac{7}{4 \cdot cos θ - sin θ}$ $r=7/(4*cos theta-sin theta)$

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

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

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