Find the slope of the line, which makes an angle of `30o` with the positive direction of yaxis measured anticlockwise.

Explanation

Let a straight line intersects `x`-axis at point `A` and `y`-axis at point `B` making `30^(@)` angle from `y`-axis in the anticlock wise direction.
Let coordinates of point `A` are `(x,0)` and coordinates of point `B` are `(0,y)`.
From figure `/_ABO=30^(@)`
Then `/_BAO=theta=90^(@)-30^(@)=60^(@)`
`implies /_BAX=120^(@)`
`:.` Slope of line ,
`m=tan120^(@)=tan(180^(@)-60^(@))`
`=-tan60^(@)=-sqrt(3)`
but slope of line from `A` t o `B`,
`m=(y-0)/(0-x)=-(y)/(x)`
`:. -(y)/(x)=-sqrt(3)` or `-sqrt(#)x=-yimpliessqrt(3)x-y=0`
Therefore, equation of required line is `sqrt(3)x-y=0`