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July 13th, 2011, 04:03 PM  #1 
Newbie Joined: Jun 2011 Posts: 8 Thanks: 0  Converting a linear graph to a linear equation?
Ok so I'm really furious, I lost a good chunk of my mark on a test I just wrote, all because one of the problems asked for something I had never done before. It wanted me to convert a linear graph into a linear equation in standard form. I have the slopeintercept form down pat, can write a graph to go along with it or vice versa no problem. Standard form is different though, I can write a graph out of a standard form equation, but I can't do it the other way around. An example of slopeintercept form being: "y = 2/3 times X + 4" While an example of Standard Form is: 3x + 2y = 6 Writing it as slopeintercept is logical because you just multiply X by the slope and then add the yintercept. Standard form is different, no matter how hard I examine a graph, I can't figure out a way to write a linear equation in the form of AX + BY = C. 
July 13th, 2011, 04:32 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 464 Math Focus: Calculus/ODEs  Re: Converting a linear graph to a linear equation?
Suppose you are given 2 points on a line: and and you are instructed to find the equation of the line written in standard form. One way to do this is to use the pointslope equation: Compute the slope m: and we have: Multiply through by Now, rearrange into standard form: Thus we see: You can of course change the signs of all 3 values if needed to avoid most of them being negative. 
July 13th, 2011, 05:19 PM  #3 
Newbie Joined: Jun 2011 Posts: 8 Thanks: 0  Re: Converting a linear graph to a linear equation?
Thanks, that clears everything up nicely. I'm still furious that the test had that question though, I really hope the teacher has the good sense to not dock me any marks, 10% off my total mark is pretty steep for something they failed to cover or even mention before.

July 13th, 2011, 05:56 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 464 Math Focus: Calculus/ODEs  Re: Converting a linear graph to a linear equation?
Let's look at the definition of slope: Given two points and Now, suppose we let the second point instead be an arbitrary point on the line (x,y), we then have: Rearranging, we find the pointslope formula for a line: Now, suppose the first point is this gives us: Solving for y, we obtain, the slopeintercept formula: Now, suppose we know the xintercept (a,0) and the yintercept (0,b). We compute the slope: Using the slopeintercept formula, we find the line is given by: Divide through by b: This is the twointercept formula for a line. If we multiply through by ab, we have: This is the line in standard form in terms of its intercepts. 

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converting, equation, graph, linear 
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