Question

How do you find the polar equation of `y=1+3x`?

Answer 1

`r=1/(sintheta-3costheta)`

Explanation:

The conversion from Rectangular to Polar:
`x=rcostheta`
`y=rsintheta`

Substitute for `x` and `y`:
`rsintheta=1+3(rcostheta)`

`rsintheta-3rcostheta=1`

Factor out the `r`:
`r(sintheta-3costheta)=1`

`r=1/(sintheta-3costheta)`