# 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 Formy - 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 - 3 may be written as follows: y - 7 = - 3 (x - 7)## 3 - Equation of a Vertical Line , where k is a constant.
x = kExample 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 , where k is a constant.
y = kExample 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 , where a, b and c are constants.
a x + b y = cExample 5: General equation of a line: 2 x - 5 y = 8## More References and Links to LineEquation of a line. Tutorial on how to find the slopes and equations of lines. Equations of Line Through Two Points And Parallel and Perpendicular. |