Slope

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Slope of a line

The slope of a line is defined as the tangent of the angle made by the line with the x-axis in the positive direction (anti-clockwise).

If q is the smallest positive angle made by the line with the x-axis, then

Slope = tanq = m.

The slope of line passing through two points A (x₁,y₁) and B (x₂,y₂).

From the above figure,

(Regardless of the quadrants in which the A and B lie.)

Example:

Find the slope and the angle of inclination q of the lines through the pairs of points (-7,-3) and (6,10).

Suggested answer:

Points are (-7,-3) and (6,10).

Slope is

Angle is