Find the tangent to the acute angle between the lines 2x ...
Find the tangent to the acute angle between the lines 2x + y = 3 and 3x - 2y = 5.
-7/4
7/8
7/4
7/2
Correct answer is C
Let ϕ be the angle between the two lines.
tan ϕ = m1−m21+m1m2
where m1 = slope of line 1; m2 = slope of line 2.
Line 1: 2x + y = 3 ⟹ y = 3 - 2x.
Line 2: 3x - 2y = 5 ⟹ -2y = 5 - 3x.
y = 32x - 52.
m1 = -2, m2 = 32.
tan ϕ = −2−321+(−2×32)
= −72−2
∴ Tan \phi = \frac{7}{4}.
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