The slope of a line is double of the slope of another line. If tangents of the angle between the is find the slopes of the other line.

Explanation

Let the slope of first line be `m_(1)` and slope of second line be `m_(2)`.
If `theta` is the angle between two lines then
`tan theta=|(m_(2)-m_(1))/(1+m_(1)m_(2))|`
But it is given that the tangent of angle `theta=(1)/(3)`
`implies (1)/(3)=|(m_(2)-m_(1))/(1+m_(1)m_(2))|`.......`(1)`
`m_(1)=2m_(2)`.......`(2)`
Put the value of `m_(1)` from equation `(2)` to equation `(1)`,
`(1)/(3)=|(m_(2)-2m_(2))/(1+2m_(2)xxm_(2))|`
`implies (1)/(3)=(+-m_(2))/(1+2m_(2)^(2))`
`implies 2m_(2)^(2)+-2m_(2)+1=0`
`implies (2m_(2)+-1)(m_(2)+-1)=0`
`implies m_(2)=+-1` or `+-(1)/(2)`
Then if `m_(2)=+-1` then `m_(1)=+-2` and if `m_(2)=+-(1)/(2)` then `m_(1)=+-1`
`:.` Slope of a line `m_(1)=+-2` or `+-1`
and slope of other line `m_(2)=+-1` or `+-(1)/(2)`
Therefore, slopes of the lines are (`+-2`or`+-1`) and (`+-1` or `+-(1)/(2)`).