A line inclined at an angle of 120° with the positive x-axis and passes through the point (4,1). Find the equation of the line.

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Solution

The slope of the line is
$m = t a n 120 °$
$m = t a n (90 + 30 °) = - c o t 30 °$
$m = - \sqrt 3$
Using the point-slope form, the equation of the line is
$y - 1 = - \sqrt 3 (x - 4)$
$y - 1 = - \sqrt 3 x + 4 \sqrt 3$
$\sqrt 3 x + y - 4 \sqrt 3 - 1 = 0$

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