Straight Lines

Definition of Slope

The slope of a straight line passing through two points ( x 1 ,    ⁢ y 1 ) and ( x 2 ,    ⁢ y 2 ) is m = y 2 − y 1 x 2 − x 1

This is also called r ⁢ i ⁢ s ⁢ e r ⁢ u ⁢ n or Δ y Δ x .

Forms of Equations of Lines

General Form: A ⁢ x + B ⁢ y = C

Slope-intercept Form: y = m ⁢ x + b

This line has slope m and y -intercept ( 0 , b ) .

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Point-slope Form: y − y 1 = m ⁢ ( x − x 1 )

This line has slope m and passes through a specified point ( x 1 ,    ⁢ y 1 ) .