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A line L passes through the point (3, −2) and makes an angle of 60° with the line √3x + y = 1. If L also cuts the x-axis, then which of the following is its equation?

1. y + √3x + 2 − 3√3 = 0
2. y − √3x + 2 + 3√3 = 0
3. √3y − x + 3 + 2√3 = 0
4. √3y + x − 3 + 2√3 = 0

Correct answer: y − √3x + 2 + 3√3 = 0

Solution

Angle 60 deg with line of slope -sqrt(3) gives slopes 0 or sqrt(3). Slope 0 (y=-2) never meets the x-axis, so take slope sqrt(3) through (3,-2): y - sqrt(3)x + 2 + 3 sqrt(3) = 0.

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