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Find the acute angle between the lines 2x + y = 4 and -3x...

Find the acute angle between the lines 2x + y = 4 and -3x + y + 7 = 0.

A.

40°

B.

44°

C.

45°

D.

54°

Correct answer is C

2x+y=4y=42xm1=2

3x+y+7=0y=7+3xm2=3

tanθ=m1m21m1m2=231(2)(3)=55=1

\tan \theta = 1 \implies \theta = 45°