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Equations of Lines in Different Forms

What are the different forms of equations of lines? Definitions and examples are presented.

The equations of lines are of the following forms:

1 - Slope intercept form:

y = m x + b


The slope intercept form is useful if the slope m and the y intercept (0, b) are known.

Example 1: The equation of a line with slope -2 and y intercept (0 , 3) is written as follows:

y = - 2 x + 3

2 - Point slope form:

y - y1 = m (x - x1).


The point slope form is useful if the slope m and a point (x
1 , y1) through which the line passes are known.

Example 2: The equation of a line that passes through the point (5 , 7) and has slope - 3 may be written as follows:

y - 7 = - 3 (x - 7)


3 - Equation of a vertical line:

x = k , where k is a constant.


Example 3: The equation of a vertical line that passes through the point (-2 , -5) may be written as follows:

x = - 2




4 - Equation of a horizontal line:

y = k , where k is a constant.


Example 4: The equation of a horizontal line that passes through the point (-2 , -5) may be written as follows:

y = - 5


5 - General equation of a line:

a x + b y = c , where a, b and c are constants.


Example 5: General equation of a line:

2 x - 5 y = 8




More on equations of lines

  • Equation of a line
  • . Tutorial on how to find the slopes and equations of lines.

  • Equations of Line Through Two Points And Parallel and Perpendicular.