Question

Find the equation of a line, whose inclination is 150° with x-axis and passes through (3, – 5)

Answer 1

Inclination of the line, \(\theta\) = 150° 

∴ Slope, m = tan(150°) = tan(90° + 60°) 

= – Cot 60° 

= – \(\frac{1}{\sqrt{3}}\) 

Since the line passes through (3, – 5) 

∴ Equation of the line is (y – y₀) = m(x – x₀) 

⇒ y − (−5) = −\(\frac{1}{\sqrt{3}}\) (x − 3) 

⇒ √3(y + 5) = x – 3 

⇒ x + √3y + (5√3 − 3) = 0, 

is the required equation of the line.