The angle between two lines is 45^ and slope of one line is 1 4 then which is the possible value of the slope of the other line.

Step-by-step solution

Let the slope of the first line be m₁ = 1 4 and the slope of the second line be m₂ . The angle between two lines with slopes m₁ and m₂ is given by the formula = | m₂ - m₁ 1 + m₁ m₂ | . Given = 45^ , we have 45^ = 1 . Substituting the values, we get 1 = | m₂ - 1 4 1 + 1 4 m₂ | . This simplifies to 1 = | 4m₂ - 1 4 + m₂ | . This leads to two cases: Case 1: 4m₂ - 1 4 + m₂ = 1 4m₂ - 1 = 4 + m₂ 3m₂ = 5 m₂ = 5 3 . Case 2: 4m₂ - 1 4 + m₂ = -1 4m₂ - 1 = -4 - m₂ 5m₂ = -3 m₂ = - 3 5 . Comparing the results with the given opti