The lines y=mx+5 and y=-3x+7 are inclined to each other at an angle of 45°. i Show that m+31-3m=1 ii Hence find the possible values of m.
i tan ϑ=m1-m21+m1m2 tan 45°=m--31+m-3 1=m+31-3m ∴ m+31-3m=1 As required ii m+31-3m=1 Or m+31-3m=-1 m+3=1-3m m+3=-1-3m 4m=-2 m+3=-1+3m m=-12 4=2m ∴m=-12 Or m=2
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