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  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:
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.

