# 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 $$(0, b)$$ of the line 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

$y - y_1 = m (x - x_1)$
The point slope form is useful if the slope $$m$$ and a point $$(x_1 , y_1)$$ through which the line passes are known.
Example 2: The equation of a line that passes through the point $$(5 , 7)$$ and has slope equal to $$- 3$$ may be written as follows:
$y - 7 = - 3 (x - 7)$

## 3 - Equation of a Vertical Line

The equation of a vertical line has the form $x = k$ 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:
$x = - 2$ Note that the slope of a vertical line is undefined.

## 4 - Equation of a Horizontal Line

The equation of a horizontal line has the form $y = k$ 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:
$y = - 5$ Its slope is equal to zero because the above equation may be written as : $$y = 0 \; x - 5$$

## 5 - General Equation of a Line

The general equation of a line may be written as $a x + b y = c$ 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.