find the inclination to x axis and intercept on y axis of the line 3y=(root3)x+6

Dear Student,

Please find below the solution to the asked query :

$$\begin{gathered} \mathrm{The} \mathrm{given} \mathrm{equation} \mathrm{of} \mathrm{the} \mathrm{line} \mathrm{is} : \\ 3\mathrm{y} = \sqrt{3}\mathrm{x} + 6 \\ \Rightarrow \mathrm{y} = \frac{1}{\sqrt{3}}\mathrm{x} + 2 ...\left(1\right) \\ \mathrm{We} \mathrm{know} \mathrm{that} \mathrm{equation} \mathrm{of} \mathrm{a} \mathrm{straight} \mathrm{line} \mathrm{having} \mathrm{slope} \mathrm{m} \mathrm{and} \mathrm{y}-\mathrm{intercept} \mathrm{c} \mathrm{is} : \\ \mathrm{y} = \mathrm{mx} + \mathrm{c} ....\left(2\right) \\ \mathrm{Comparing} \left(1\right) \mathrm{and} \left(2\right), \mathrm{we} \mathrm{get} \\ \mathrm{m} = \frac{1}{\sqrt{3}} \mathrm{and} \mathrm{c} = 2 \\ \Rightarrow \tan \mathrm{\theta } = \frac{1}{\sqrt{3}} \mathrm{and} \mathrm{y}-\mathrm{intercept} = 2 \\ \Rightarrow \mathrm{\theta } = 30° \mathrm{and} \mathrm{y}-\mathrm{intercept} = 2 \\ \Rightarrow \mathrm{inclination} = 30° \mathrm{and} \mathrm{y}-\mathrm{intercept} = 2 \end{gathered}$$

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