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Mathematics

Find the equation of a line whose inclination is 30° and whose y-intercept is –2.

Straight Line Eq

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Answer

Given,

θ = 30° and c = -2.

We know that,

m = tan θ = tan 30° = 13\dfrac{1}{\sqrt3}.

Substituting values of m and c in equation y = mx + c, we get :

⇒y=13x+(−2)⇒3y=x−23⇒3y−x+23=0.\Rightarrow y = \dfrac{1}{\sqrt3} x + (-2) \\[1em] \Rightarrow \sqrt3y = x - 2\sqrt{3} \\[1em] \Rightarrow \sqrt3y - x + 2\sqrt{3} = 0.

Hence, equation of the line is 3y−x+23\sqrt3y - x + 2\sqrt{3}.

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