Coordinate Geometry

To find the possible slopes of lines that make a 60° angle with the given line, we follow these steps:

1. Determine Original Slope:
Given line equation:
Convert to slope-intercept form:
→ Slope

2. Angle Between Lines Formula:
For two lines with slopes and making angle θ:

Given θ = 60° and :

3. Solve for Possible Slopes:
This absolute value equation gives two cases:

Case 1:

Solving yields:

Case 2:

Solving yields:

Final Answer:
The possible slopes are:
and