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
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