Convert to Polar 9x+y=10

$9 x + y = 10$

Since $x = r \cos (θ)$ , replace $x$ with $r \cos (θ)$ .

$9 (r \cos (θ)) + y = 10$

Since $y = r \sin (θ)$ , replace $y$ with $r \sin (θ)$ .

$9 (r \cos (θ)) + r \sin (θ) = 10$

Solve for $r$ .

Simplify the left side.

Remove parentheses.

$9 r \cos (θ) + r \sin (θ) = 10$

Factor $r$ out of $9 r \cos (θ) + r \sin (θ)$ .

Factor $r$ out of $9 r \cos (θ)$ .

$r (9 \cos (θ)) + r \sin (θ) = 10$

Factor $r$ out of $r \sin (θ)$ .

$r (9 \cos (θ)) + r (\sin (θ)) = 10$

Factor $r$ out of $r (9 \cos (θ)) + r (\sin (θ))$ .

$r (9 \cos (θ) + \sin (θ)) = 10$

Divide each term in $r (9 \cos (θ) + \sin (θ)) = 10$ by $9 \cos (θ) + \sin (θ)$ and simplify.

Divide each term in $r (9 \cos (θ) + \sin (θ)) = 10$ by $9 \cos (θ) + \sin (θ)$ .

$\frac{r (9 \cos (θ) + \sin (θ))}{9 \cos (θ) + \sin (θ)} = \frac{10}{9 \cos (θ) + \sin (θ)}$

Simplify the left side.

Cancel the common factor of $9 \cos (θ) + \sin (θ)$ .

Cancel the common factor.

$\frac{r (9 \cos (θ) + \sin (θ))}{9 \cos (θ) + \sin (θ)} = \frac{10}{9 \cos (θ) + \sin (θ)}$

Divide $r$ by $1$ .

$r = \frac{10}{9 \cos (θ) + \sin (θ)}$