# How do you convert -2x + 6y = 7 to polar form?

Jul 9, 2016

$r = \frac{7}{6 \sin \theta - 2 \cos \theta}$

#### Explanation:

To convert from $\textcolor{b l u e}{\text{cartesian to polar form}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{x = r \cos \theta , y = r \sin \theta} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Substituting into cartesian equation

$\Rightarrow - 2 \left(r \cos \theta\right) + 6 \left(r \sin \theta\right) = 7$

$\Rightarrow - 2 r \cos \theta + 6 r \sin \theta = 7$

$\Rightarrow r \left(6 \sin \theta - 2 \cos \theta\right) = 7$

$\Rightarrow r = \frac{7}{6 \sin \theta - 2 \cos \theta} \text{ is the polar form}$