SLOPE OF A LINE

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Slope of a line

  • A line in a coordinate plane forms two angles with the x-axis, which are supplementary. 
  • The angle θ made by the line l with positive direction of x-axis and measured anti-clockwise is called the inclination of the line. Obviously 0° ≤ θ ≤ 180°.
  • We observe that line parallel to x-axis, or coinciding with x-axis, have inclination of 0°. 
  • The inclination of a vertical line ( parallel to or coinciding with y-axis ) is 90°.
If θ is the inclination of a line l, then tanθ is called the slope or gradient of the line l. The slope of a line having inclination 90° 
is not defined.

 The slope of a line is denoted by m.

Thus m = tanθ, θ ≠ 90°.

It may be observed that slope of x-axis is zero and slope of y-axis is not defined.

Slope of a line when coordinates of any two points on the line are given 

Let P ( x, y ) and Q ( x, y ) be two points on a line l with inclination θ. Then slope is given by








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