Question

Find equation of the line through the point (0, 2) making an angle 2π/3 with the positive x - axis. Also, find the equation of line parallel to it and crossing the y - axis at a distance of 2 units below the origin.

Answer 1

Answer:

• y = -√3x +2
• y = -√3x -2

Step-by-step explanation:

You want lines making an angle of 2π/3 with the +x axis and passing through the points (0, 2) and (0, -2).

Slope-intercept form

The slope of the line is the tangent of the angle:

  m = tan(2π/3) = -√3

The given points are the y-intercepts: 2 and -2, respectively. The slope-intercept equation for a line is ...

  y = mx +b . . . . . . . where m is the slope and b is the y-intercept

The equations for the lines are ...

 y = -√3x +2 . . . . . . through point (0, 2)

  y = -√3x -2 . . . . . . crossing 2 units below the origin