If the angle between two lines is `pi/4`and slope of one of the lines is `1/2`, find the slope of the other line.

Explanation

Here `theta=pi//4` and `m_(1)=1//2`
Let the slope of second line be `m_(2)`.
Noe, `tan theta=|(m_(2)-m_(1))/(1+m_(1)m_(2))|`
`implies tan45^(@)=|(m_(2)-(1)/(2))/(1+(1)/(2)m_(2))|`
`implies +-1=(2m_(2)-1)/(2+m_(2))`
`implies 1=(2m_(2)-1)/(2+m_(2))` or `-1=(2m_(2)-1)/(2+m_(2))`
`implies2m_(2)-1=2+m_(2)` or `2m_(2)-1=-2-m_(2)`
`implies m_(2)=3` or `m_(2)=-(1)/(3)`
Therefore, the slope of other line is `3` or `-(1)/(3)`