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Mathematics

The inclination of the line 3x−3y+7\sqrt{3}x - 3y + 7 = 0 is :

  1. 30°

  2. 45°

  3. 60°

  4. 75°

Straight Line Eq

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Answer

Given, equation :

⇒3x−3y+7=0⇒3y=3x+7⇒y=33x+73⇒y=13x+73.\Rightarrow \sqrt{3}x - 3y + 7 = 0 \\[1em] \Rightarrow 3y = \sqrt{3}x + 7 \\[1em] \Rightarrow y = \dfrac{\sqrt{3}}{3}x + \dfrac{7}{3} \\[1em] \Rightarrow y = \dfrac{1}{\sqrt{3}}x + \dfrac{7}{3}.

Comparing above equation with y = mx + c, we get :

⇒ m = 13\dfrac{1}{\sqrt{3}}

⇒ tan θ = tan 30°

⇒ θ = 30°.

Hence, Option 1 is the correct option.

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