Linear equations can be written in several forms. Each form has its pros and cons as to why we would want to express the equation in such a format. This is because certain information about the line and the linear relationship it represents can be easily identified just by looking at its equation. The first form is slopeintercept form.
The equation of a line written in slopeintercept form is:
We refer to this form as slopeintercept form, because the equation readily gives us information about the line's slope, and its yintercept. The variable represents slope, and the variable represents the ycoordinate of the yintercept (remember that the xcoordinate of a yintercept is always zero).
Here is an example of an equation written in slope intercept form:

Slope intercept form  

The line has a slope of 8  

The yintercept is at (0, 3)  
 

(0, 3) = (x, y)  

Multiply 8 by 0  

Add 0 to 3 
In the second part of the example above, we used the coordinate point (0, 3) which is our yintercept, to confirm that everything is correct. Since 3 = 3 is a true statement, we have correctly identified 8 as the slope, and (0, 3) as the location of the yintercept.
Linear equations can also come written in PointSlope form. PointSlope form, as the name suggests, provides information about the lines slope, and a point on the line. PointSlope form is as follows:
Once again, we can easily identify the line's slope by the variable m. Here, we also have and . These represent the xcoordinate and ycoordinate of a point on a line. Below is an example of a linear equation written in PointSlope form:
This tells us that the line has a slope of 3, and that the point (2, 7) is a point on the line.
A final form we will discuss today is called Standard Form. Unlike slopeintercept form, or pointslope form, we cannot readily identify the slope, yintercept, or point on a line simply by looking at the equation in standard form. However, the benefit of standard form is that any linear equation can be written in standard form, whereas not every line can be written in slopeintercept or pointslope forms. Think about a vertical line. It is an undefined slope. Both slopeintercept and pointslope forms rely on a defined slope to generate its equation. A vertical line, however, can be written in standard form, because a slope is not needed to write its equation.
Here is the standard form for a linear equation:
A couple of notes about general accepted rules for equations written in standard form: