Find the equation of the lines through the point (3, 2) which make an angle of `45^o` with the line `x-2y=3`.

Explanation

Equation of given line , `x-2y=3`
Its slope, `m=-(1)/(-2)=(1)/(2)`
Slope of lines making `45^(@)` angle from this line
`=(m+-tan45^(@))/(1overset(-)(+)m tan45^(@))=((1)/(2)+-1)/(1overset(-)(+)(1)/(2))`
`=((1)/(2)+1)/(1-(1)/(2))` or `((1)/(2)-1)/(1+(1)/(2))`
`=3` or `-(1)/(3)`
Now equation of l ine passing through the point `(3,2)` and of slope `3` is ,
`y-2=3(x-3)`
`implies y-2=3x-9`
`implies 3x-y=7`
Now, equation of a line passing through the point`(3,2)` and of slope `-(1)/(3)` is
`y-2=-(1)/(3)(x-3)`
`implies 3y-6=-x+3`
`implies x+3y=9`
`:.` Required equations are
`3x-y=7` and `x+3y=9`