(α,β) lie on line 3x+y=0 ⇒‌‌3α+β=0 ‌β=−3α....(i) Substitute (3,4) in the expression, 3x−4y−8 ⇒3×3−4×4−8=9−16−8<0 ⇒3α−4β−8>0 ‌[∵(α,β)‌ and ‌(3,4)‌ lie on opposite side] ‌ ⇒3α−4(−3α)−8>0 ⇒3α+12α−8>0 ∴‌15α−8>0