A straight line makes an angle of 30° with the positive x-axis and cuts the...

JAMB 2001

A straight line makes an angle of 30° with the positive x-axis and cuts the y-axis at y = 5. Find the equation of the straight line.

A. y = (x/10) + 5
B. y = x + 5
C. √3y = - x + 5√3
D. √3y = x + 5√3

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Correct Answer: Option D

Explanation

Cos 30 = 5/x
x cos 30 = 5, => x = 5√3

Coordinates of P = -5, 3, 0
Coordinates of Q = 0, 5
Gradient of PQ = (y₂ - y₁) (X₂ - X₁) = (5 - 0)/(0 -5√3)
= 5/5√3 = 1/√3

Equation of PQ = y - y₁ = m (x -x₁)
y - 0 = 1/√3 (x -(-5√3))

Thus: √3y = x + 5√3

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