In Exercises, find the equation of the line which satisfy the given conditions:Passing through and inclined with the x-axis at an angle of 75o.

Given point = (2, 2√3) and θ = 75°

Equation of line: (y - y1) = m (x - x1)
where, m = slope of line = tan θ
and (x1, y1) are the points through which line passes

m = tan 75°

75° = 45° + 30°

Applying the formula:

Rationalizing we get,

We know that the point (x, y) lies on the line with slope m through the fixed point (x1, y1), if and only if, its coordinates satisfy the equation y – y1 = m (x – x1)

y 23 = (2 + √3) (x – 2)

y 23 = 2 x - 4 + √3 x - 2 √3

y = 2 x - 4 + √3 x

(2 + 3) x y - 4 = 0

Ans. The equation of the line is (2 + √3) x – y - 4 = 0.

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