# How do you graph r=12/(-4costheta+6sintheta)?

Mar 22, 2018

Draw a line with a $y$-intercept of $2$ and a gradient of $\frac{2}{3}$

#### Explanation:

Multiply each term by $\left(- 4 \cos \theta + 6 \sin \theta\right)$

$r \left(- 4 \cos \theta + 6 \sin \theta\right) = 12$

$- 4 r \cos \theta + 6 r \sin \theta = 12$

$- 2 r \cos \theta + 3 r \sin \theta = 6$

$r \cos \theta = x$
$r \sin \theta = y$

$- 2 x + 3 y = 6$
$y = \frac{2 x + 6}{3} = \frac{2 x}{3} + 2$

Draw a line with a $y$-intercept of $2$ and a gradient of $\frac{2}{3}$

Mar 22, 2018

I use the Desmos Graphing Calculator; it is a free online graphing tool that anyone can use.

#### Explanation:

One thing that I do not like about the calculator is that it requires that polar equations be in the form $r = f \left(\theta\right)$; it will graph your equation very well but it will not graph something like the following:

${r}^{2} = r \sin \left(\theta\right) + 5$

It does not have this requirement for Cartesian equations.

I like that you can graph multiple equations and you can select the colors that you like.

I wish that it did 3d plots but you can't have everything for free.

You can make a user-id and I have one but I found that you have all of the features except the ability to save your work without logging on.