# What is the need to define so many forms of equation of a straight line?

When I study maths, I try to understand why the mathematicians brought out this concept or what usefulness they might have seen in the concept that they worked upon. So when I started with straight lines, what hit me was that why do we have to have so many forms of equations of straight lines? All they do is just help make more questions but don't really help us in real life applications of straight line concepts (or do they?). What was the need to explicitly define those forms? Why not only one general form was defined?

• Could you mention some examples?
– zoli
Jun 6, 2015 at 11:27
• Short answer: Each version of an equation of a line is useful to some people at some times. For example, I made a payroll spreadsheet calculating income tax for employees in Kenya and succeeded where many others failed because I used the point-point form of the equation of a line. Jun 6, 2015 at 11:34
• Which forms do you believe have no "real life applications"? Certainly all of the usual ones are useful in various contexts. Jun 6, 2015 at 11:36
• For example, 3x+y-2=0 is the equation of a straight line in its general form then from this the fact that y= -3x+2( which is the slope intercept form) is implied and can be used as per our convenience. What made mathematicians define that explicitly as a totally different form? (looking from its mathematical applications point of view) Jun 6, 2015 at 11:36
• The slope intercept form cannot be generalized to, say, three dimensions. Neither the $ax+bx+c=0$ could be generalized. ($ax+bx+cz+d=0$ would be a plane.) However, if $a=(u,v)$ and $b=(e,f)$, $z=(x,y)$ are vectors then $z=ta+b$ is a dimension independent form for straight lines. ($t$ is a real parameter).
– zoli
Jun 6, 2015 at 11:48