
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
July 13th, 2011, 03:03 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, 03:32 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 462 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, 04:19 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, 04:56 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 462 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. 

Tags 
converting, equation, graph, linear 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Linear approximation of Non linear system by Taylor series  RGNIT  Calculus  0  March 20th, 2014 11:21 PM 
Advantages of using intercepts to graph linear equations  chelsf123  Algebra  1  August 26th, 2013 08:20 AM 
Solve nonlinear system (=linear+linear systems)  tools  Linear Algebra  1  September 21st, 2012 12:38 PM 
linear equation  555  Algebra  1  November 13th, 2010 11:13 AM 
TI 86 Cal Help! Urgent.Pls Help. To Graph Linear Programming  animallover1  Math Software  0  November 2nd, 2010 09:48 PM 