MATH N 223 INCLINATION and SLOPE

INCLINATION and SLOPE  

Definition of terms:
1.    Angle of inclination – is the least counterclockwise
         angle from the positive x-axis to the line.

  2. Slope(m) – is the tangent of the angle of inclination.

     m = tan α
        m =(y₂ – y₁) / (x₂ - x₁)
         where x₂ is not = x₁)
 

Notes :
  a) A line sloping upward to the right has a positive
       slope.
  b) A line sloping downward to the right has a negative
       slope.
  c) The slope of a line parallel to the x-axis is zero.
  d) The slope of a line parallel to the y-axis is
       undefined.

PARALLEL AND PERPENDICULAR LINES

Theorem 1: Two lines are parallel if and only if their
            slopes are equal.

          m₁ = m₂
         
          where :
         m₁ = is the slope of the line L₁
         m₂ = is the slope of the line L₂

Theorem 2: Two lines are perpendicular if and only if their
         slopes are negative reciprocals.

         m₁ = -1/m₂

        or (m₁)(m₂) = -1