Friday, January 16, 2009

Converting Point-Slope Form to Standard Form

I previously described how to obtain the equation of a line, and how to express that in both point-slope form and standard form. While both equations describe the exact same line, sometimes you may be asked to express the line in a specific way, and you need to be able to manipulate and rearrange the provided equation to make it look like the other form. I will show an example of how this can be done.  (Please hit the Like and/or Google +1 button at the bottom if you find this helpful!)

Reminders (refer to the posts linked above for more details)

Point-slope form looks like this:
(y-y1) = m(x-x1), which is the general way of saying y=mx+b

Standard form looks like this:
Ax + By = C

Example: Express the equation y=5x-10 in standard form. State the values for A, B, and C.

Basically, what you want to do is move all the x and y terms over to one side, and move the constants (terms with no variables) over to the other. Combine and simplify where possible. That's all there is to it. "A" will be the term left over in front of x, "B" will be with y, and C will be the value not attached to a variable.

A=5, B=(-1), C=10
(remember the standard form has a "+", so a "-" in your answer implies a coefficient of (-1).

Let's try another one:

Express the equation y=(4/3)x+2 in standard form. State the values for A, B, and C.

This one works the same way, but there is something else that can be done, as I will demonstrate.

A=(4/3), B=(-1), C=(-2)
There is nothing wrong with this answer. It is properly rearranged, and the coefficients have been stated. However, usually it is a good idea to not have fractions (ie. have nothing in the denominator). So, to do this, you work our final answer a bit further, so that all the values are in the numerators.

Multiply all terms by 3, to remove it from the denominator of the first term. This gives:
A=4, B=(-3), C=(-6)

Again, this answer describes the exact same line as the initial answer without the extra moves, so technically, they are both right. It is just a common convention to keep things in the numerator wherever possible.  Please hit the Like or Google +1 button below if this helped you.  :)

Converting from the Standard Form to the Point-slope form is basically just the reverse. Try it for yourself with these examples!


  1. thanks dude, i needed this for math haha

  2. Thank you!!!!!!!

  3. This helped out alot!!

  4. ummm when the standard form is
    Ax+By+C = 0 how does the problem change? im so confused because the way its being tought in class the equation is not equal to C

  5. I think you're probably dealing with one of the common types of problems, and that is solved by simply rearranging the equation you have. If you have most of the equation on one side, and it is equal to some number other than 0, just move that number to the side with the x and y to make the expression equal 0, rearrange if necessary, and you will likely have solved it in standard form.

  6. Thanks, I was so confused. Nice guide btw

  7. Thank you sooooo much. I appreciate it dearly!

  8. This helped a ton. Thanks a bunch!

  9. this helped sooooooooooo much and its also correct thank a whole lot. this website is corect

  10. oh my gosh THANK YOU!!!!!!!!

  11. I just passed my math final because of this omg thank u soo so so soo much :)

  12. wow, thank you!!! i've been trying to wrap my head around this conversion far about an hour now and this helped ALOT. thank you

  13. Thanks man, this is a big help. It is a shame that most lectures are given one way then the problems are given/ask in the reverse order. This really helps.

  14. Thanks man, this really helped. It is really messed up how most of our lectures are given one way then when you attempt the problems they are the reverse. Equation to graph is easy, but graph to standard form equation is not covered very well until now. Thanks again.

  15. this helps a little

  16. thank you a lot hopefully my grade goes from a 72 to a 83. :}

  17. Thank you for your help, I'm struggling in Algebra Honors and being an 8th grader taking this class is hard for me, So thank you for your help on this.

  18. thanks! This helps a lot! I am taking an advanced course (which is algebra) in 7th grade and our teacher is very vague when explaining how to solve equations such as these. Thanks SOOOOOOOOOOOOOOOOOOO much!!!!! =D

  19. You have made it sooooooo easy to understand. Thank you

  20. Dude -- Great job on showing how converting between these two forms of the line can be done quickly, easily, and thankfully pain-free!! Question: My recollection, at least from my experience here in the States is that y = mx + b is often referred to specifically as "slope-intercept" form, whereas "point-slope" form (which incidentally I find, these days, I use less and less), was reserved for specifically the equation you noted above, y-y1=m(x-x1). Do they use this "slope-intercept" terminology up north as well? Or is something we Yankees dreamt up to use only for ourselves! ;-)

    1. Keith Roberts -
      Thanks for you message! It's nice to know that some people find my posts helpful! I agree with what you say about slope-intercept and point-slope terminology. Slope-intercept means the same thing here in Canada as is does down below the border. ;) I think I should have probably focused more on point-slope form in the examples, though I do note up near the beginning that point-slope is a generic form of y=mx+b... I appreciate your comment about it! I'm actually redoing several of these blog posts on my new site, I'd love to have you and everyone else check out that site and give me your thoughts on how it's looking so far!

  21. VERY HELPFUL!!!! :D


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