Changing from Slope-Intercept to Standard Form
Date: 06/02/2005 at 00:35:36 From: Tiffani Subject: standard form Ax+By+C=0 Hi Doctor Math. I know a little about standard form, but I am having a hard time going from slope-intercept form to standard form. I'm trying to do a line with a slope of -2/3 and a y-intercept of 8/3, so I know the slope-intercept form is y = (-2/3)x + 8/3. But how do I get that into Ax + By + C = 0 form? If you can help me, I would greatly appreciate it.
Date: 06/02/2005 at 23:05:57 From: Doctor Peterson Subject: Re: standard form Ax+By+C=0 Hi, Tiffani. The process is something like how you solve an equation, but in reverse. In solving an equation, you want to transform it into an equivalent equation of the form "y = ?", which you do by taking a series of steps that gradually get y by itself. What you want to do here is to transform it into an equation of the form "?x + ?y + ? = 0", which means that x and y and the constant are all on the same side, rather than one variable being alone on the right. Let's take an example. Say we're given y = (1/2)x - 2/5 We want x, y, and the constant on the same side, so let's just subtract y from both sides and we get 0 = (1/2)x - y - 2/5 Everything looks right except that the zero is on the left; I've already arranged for the terms on the right to be in the right order. So we can just write (1/2)x - y - 2/5 = 0 Now, there's one thing we can do to make this look nicer; we'd like A, B, and C to be whole numbers rather than fractions, since fractions complicate things. To eliminate fractions, we can multiply the whole equation by the LCD, which is 10. Do that, and we get (10/2)x - 10y - 20/5 = 0 5x - 10y - 4 = 0 And we're done! It was really pretty easy: subtract y from both sides and then multiply by the LCD. But more important than the specific steps is the basic principle, which applies to many kinds of problems: visualize the form you want to end up with, then do one step at a time to get it that way. We first saw that the y was not with the other terms, so we fixed that; then we fixed up the order; and then we got rid of fractions, which were not part of our image of the ideal "standard" form. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 06/02/2005 at 23:43:48 From: Tiffani Subject: Thank you (standard form Ax+By+C=0) Thank you Dr. Math, I think I finally understand it. If I have any more problems, I'll be sure to ask but this was very helpful. Thanks again.
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