# Find the equation of a line whose inclination with the x

Question:

Find the equation of a line whose inclination with the $x$-axis is $30^{\circ}$ and which passes through the point $(0,5)$.

Solution:

As angle is given so we have to find slope first given by m = tanθ

$m=\tan 30^{\circ}$

$\mathrm{m}=\frac{1}{\sqrt{3}}$

Now the line is passing through the point (0, 5).using slope - intercept form of the equation of the line, we will find the intercept

$y=m x+c$ ................(1)

$5=\frac{1}{\sqrt{3}}(0)+\mathrm{c} \Rightarrow \mathrm{c}=5$

Putting the value of c in equation (1),we have

$y=\frac{1}{\sqrt{3}} x+5$

$x-(\sqrt{3}) y+5 \sqrt{3}=0$

So, required equation of line is $x-(\sqrt{3}) y+5 \sqrt{3}=0$

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