The straight line L≡x+y+1=0 and L1≡x+2y+3=0 are intersecting, m is the slope of the straight line L2 such that L is the bisector of the angle between L1 and L2. The value of m2 is.

Let the equation of L2 be L1+λL=0⇒(1+λ)x+(2+λ)y+(3+λ)=0Slope of L2,Land L1 are −1+λ2+λ,−1,−12Since L is the bisector of the angle between L1 and L2 ∴−1+λ2+λ+11+1+λ2+λ=−1+121+12⇒λ=−3So the equation of L2 is y+2x=0⇒m=−2