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 References and Links to Line


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.

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