The slope of lines which makes an angle 60^ with the line y-3 x+18=0

Step-by-step solution

The given line is y - 3x + 18 = 0 , which can be written as y = 3x - 18 . The slope of this line is m₁ = 3 . Let the slope of the required lines be m . The angle between the two lines is given by = | m - m₁ 1 + m m₁ | . Given = 60^ , we have 60^ = 3 . Substituting m₁ = 3 , we get 3 = | m - 3 1 + 3m | . This leads to two cases: m - 3 1 + 3m = 3 or m - 3 1 + 3m = - 3 . Case 1: m - 3 = 3 + 3m 3 m(1 - 3 3 ) = 3 + 3 m = 3 + 3 1 - 3 3 . Case 2: m - 3 = - 3 - 3m 3 m(1 + 3 3 ) = 3 - 3 m = 3 - 3 1 + 3 3 . Comparing these re