# Equations of Lines in Different Forms

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

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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.