Given: A line which makes an angle of \[{{150}^{o}}~\]with the x–axis and cutting off an intercept at \[2\]

By using the formula,

The equation of a line is \[y\text{ }=\text{ }mx\text{ }+\text{ }c\]

We know that angle, \[\theta \text{ }=\text{ }{{150}^{o}}\]

The slope of the line, \[m\text{ }=\text{ }tan\text{ }\theta \]

Where, \[m\text{ }=\text{ }tan\text{ }{{150}^{o}}\]

\[=\text{ }-1/~\surd 3\]

Coordinate of y–intercept is \[\left( 0,\text{ }2 \right)\]

The required equation of the line is \[y\text{ }=\text{ }mx\text{ }+\text{ }c\]

Now substitute the values, we get

\[y\text{ }=\text{ }-x/\surd 3\text{ }+\text{ }2\]

\[\surd 3y-2\surd 3\text{ }+\text{ }x\text{ }=\text{ }0\]

So,

\[x\text{ }+~\surd 3y\text{ }=\text{ }2\surd 3\]

∴ The equation of line is \[x\text{ }+~\surd 3y\text{ }=\text{ }2\surd 3\]