Monday, April 9, 2007

Graphing - Standard Form of the Equation

Just a short explanation for what is meant by "standard form" of the equation of the line. We have been looking at line equations in the form of y=mx+b. However, you may be asked to express this in standard form, or as a standard form equation.  Graphing standard form equations will give you the exact same line as graphing something expressed as y=mx+b... standard form is just a different way of displaying the equation.  (Please hit the Like button and/or the +1 button if this post is helpful for you!)

The general notation for a standard form equation is Ax + By = C, where A, B, and C are coefficients, and the x and y are the same variables we've been looking at but in a different position from what we recognize.

To express in standard form, you simply just rearrange the y = mx + b form such that you have x and y on the same side, equal to a number. Let's look at some examples:

Given that y = 3 x+ 5, standard form of this is 3x - y = (-5).

Given y = (1/2)x -15, standard form of this is (1/2)x - y = 15... also, if you don't want to have any fractions in your answer, you can multiply everything by the number in the denominator, such that we now get x - 2y = 30. Both expressions mean the same thing and will produce the same line. (In fact, convince yourself that no matter what you do to the equation, so long as you do it to both sides, the line is the same. eg. Multiply it all by 100, you get 100x-200y=30000... looks different, but it's not! Reduce it down and see for yourself!)

For graphing standard form equations, you still might want to go from standard form to the mx+b form, for which you may need to do a bit more math, but it's still quite straight forward.

Given 5x - 15y = 10, you just have to rearrange things to get y by itself on one side:
(-15y) = (-5x) + 10
y = (1/3)x - (2/3)...
and then you can see it is a line with slope 1/3 and y-intercept (-2/3).

Both types of equations mean the same thing. They are just expressed differently, and y=mx+b gives immediate information about the line without having to do a lot of work. However, you should be able to use both forms interchangeably.  Convince yourself that graphing standard form equations will give you the same line as graphing y=mx+b equations.  They just look different because the numbers are rearranged.  This should be obvious because if you start with a standard form equation, and convert it to y=mx+b and graph it, you have only rearranged things not added or removed anything.  You do not have a new line.

Also, from these equations, you should be able to tell that whenever you have an equation with 2 variables (x and y), and there aren't any exponents on either term, then you are dealing with a straight line. So while an equation in standard form may not immediately look like a straight line equation to you until it looks like y = mx + b, because it has an x and a y in it (without an exponent... exponents make the graph do cool things later), it is automatically a straight line.

(check this post for some additional pointers)

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  1. hi!

    The blog looks great!

    I've written a post directing people to your site, but I can't for the life of me get a link posted.

    For some reason I'm having a terrible time posting links to other Blogger blogs. I get a message saying that the link is taking too long, so the site is aborting.

    Are you having the same problem?

    Catherine Johnson
    kitchen table math the sequel

  2. Great site!

    I've added you to my blogroll.

  3. THANKS FOR THIS im working on my algebra project and this helped me understand this better ive got to make a book explaining about every way to graph

  4. Thanks for this. It really helped me on my Algebra 2 project. Im supposed to write down 10 formulas and esplain the 10 things given about each one. This really helped!

  5. Thanks.
    This helped a lot!

  6. Thanks this helped me, but you left out how to get from point-slope to standard.... but other than that it was great! Thanks!!!

  7. I've added a new post at that hopefully might be of some use to you! Thanks for the comments!

  8. thanks alot for this :)

  9. how would yopu turn this into standard form - (8,3) M=4?

  10. (8,3), m=4

    The easiest way to do this is to punch these numbers into y=mx+b form first.


    Knowing b, you can rewrite the equation:


    For standard form, you just have to rearrange so that everything is on the one side:


    That's it!

  11. I could propose to you right now!! But I won't because that would creep you out. Thanks I was about to explode.

  12. Thanks a bunch! I was stuck on my math hw until i saw this!

  13. You just helped me earn an one hundered percent on my math homework!

  14. okay, i'm only 15, i've got so many questions...

    okay my homework paper says...WRITE THE STANDARD FORM OF EACH EQUATION..

    the equations are:






    9 don't know how to do any of them...

    please help me!!!!!!!!!!!!

  15. For these questions, all you need to do is simplify. First, you multiply to get rid of the brackets. Then, you combine any like-terms. Finally, you just rearrange the terms into standard form.

    I'll try the first one with you, so that you can get the hang of it:

    y+5=3(x-2)... get rid of the brackets
    y+5=3x-6... combine like-terms
    y=3x-11... rearrange to standard form

    Do the same thing to the others and you will have your answers. Good luck!

  16. Thanks for this! It has helped me a lot for my test :)

  17. Merci beaucoup. Tu as aide moi beaucoup!

  18. Thank You a ton! I couldn't figure out how to graph point slope for my algebra homework but now I can!

  19. How do I determine the standard form of the equation if the question is asking me..."write the standard form of the equation of the line through the given point with the given slope---through: (4,0), slope=-1/2?"

  20. How do I determine the standard form of the equation if the question is asking me..."write the standard form of the equation of the line through the given point with the given slope---through: (4,0), slope=-1/2?"

    Well, you have an ordered pair that is on the line, so you know one value for x and it's corresponding y. You also have the slope of the line. So, you have everything you need to solve for the y-intercept, b. So, plug all those numbers into y = mx + b, and solve for b.

    Then, once you have b, you can write the equation of the line in terms of x and y, with m and b as values this time. Finally, rearrange everything so that it is presented in standard form, ie. everything is on one side and equals 0.

    Let me know if you get it or you'd like me to work through the numbers!

  21. Thx man-
    im not that good in school and after listening to my teacher at my middle school ramble and ramble in an alein language that inever understood, its nice to know taht te internet has sites like this with simple languge and to-the-point text to teach me in 5 minutes what my teacher hasnt gotten across in days. Sad wheres educations come to.


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