Show that the equation of the straight line through the origin angle `varphi` with the line `y=m x+b\ i s y/x=(m+-t a nvarphi)/(1+-m\ t a nvarphi)`

Explanation

Slope of given line `=m`
If `m_(1)` is the slope of a line making angle `theta` from this line then
`tan theta=|(m-m_(1))/(1+mm_(1))|`
`implies +-tan theta=(m-m_(1))/(1+mm_(1))`
`implies m-m_(1)=+-tantheta+-mm_(1)tantheta`
`implies m+-tantheta=m_(1)(1+-m tan theta)`
`implies m_(1)=(moverset(-)(+)tantheta)/(1+-mtantheta)=(m+-tantheta)/(1overset(-)(+)mtantheta)`
Now, equation of line passing through origin and of slope `m_(1)` is,
`y-0=m_(1)(x-0)`
`implies y=m_(1)x`
`implies (y)/(x)=m_(1)`
`implies(y)/(x)=(m+-tan theta)/(1overset(-)(+)m tantheta)`