document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=36593>Question 36593</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Why is it true that any two points satisfying a linear equation will give you the same graph for the line represented by the equation?\r<BR>\n" );
document.write( "\n" );
document.write( "Please Help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #22484 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=22484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Why is it true that any two points satisfying a linear equation will give you the same graph for the line represented by the equation?<BR>\n" );
document.write( "Please Help...WELL THE ANSWER IS IN YOUR QUESTION ITSELF!!LET ME ELABORATE...<BR>\n" );
document.write( "FIRSTLY WE SHOULD UNDERSTAND WHAT IS A GRAPH,WHAT IS ITS EQUATION AND VICEVERSA..<BR>\n" );
document.write( "AND WHAT IS MEANT BY SATISFYING AN EQUATION.<BR>\n" );
document.write( "1.WE SAY A POINT SATISFIES AN EQUATION WHEN ITS COORDINATES ARE SUBSTITUTED IN THE EQUATION MAKES ITS RHS EQUAL ITS LHS.<BR>\n" );
document.write( "2.WE SAY A POINT DOES NOT SATISFY AN EQUATION WHEN ITS COORDINATES ARE SUBSTITUTED IN THE EQUATION DOES NOT MAKE ITS RHS EQUAL ITS LHS.<BR>\n" );
document.write( "NEXT....<BR>\n" );
document.write( "1.WE SAY A GRAPH IS REPRESENTED BY AN EQUATION OR THE GIVEN EQN.IS FOR A PARTICULAR GRAPH,WHEN THE POINTS OBTAINED AS ABOVE FROM THE GIVEN EQN.,ARE PLOTTED AND JOINED      <BR>\n" );
document.write( "BY A LINE ,THEY FORM THE GRAPH UNDER CONSIDERATION\r<BR>\n" );
document.write( "\n" );
document.write( "THESE APPEAR TO BE ELEMENTARY ,BUT THEY STIPULATE 4 IMPORTANT CONSIDERATION AT THE SAME TIME WHICH WILL ANSWER YOUR QUESTION...THEY ARE <BR>\n" );
document.write( "GIVEN AS MENTIONED ABOVE AN EQUATION AND ITS GRAPH.....THEN....<BR>\n" );
document.write( "1.IF A POINT SATISFIES THAT EQN. THEN IT LIES ON THE GRAPH.<BR>\n" );
document.write( "2.IF A POINT DOES NOT SATISFY THAT EQN. THEN IT DOES NOT LIE ON THE GRAPH.<BR>\n" );
document.write( "3.IF A POINT IS ON THE GRAPH,THEN IT SATISFIES THE EQN.<BR>\n" );
document.write( "4.IF A POINT IS NOT ON THE GRAPH,THEN IT DOES NOT SATISFY THE EQN.\r<BR>\n" );
document.write( "\n" );
document.write( "WITH THE ABOVE UNDERSTANDING LET US ANSWER YOUR DOUBT.<BR>\n" );
document.write( "THE EQN. IS A LINEAR EQN.YOU WILL SOON LEARN THAT GRAPH OF A LINEAR EQN.IS A STRAIGHT LINE.<BR>\n" );
document.write( "SO ONCE IT IS GIVEN THAT THE EQN.IS LINEAR IN X AND Y IT AUTOMATICALLY IMPLIES THAT THE GRAPH IS A STRAIGHT LINE IN PLANE GEOMETRY.<BR>\n" );
document.write( "NOW WE KNOW THAT WE NEED ONLY 2 POINTS TO FIX A STRAIGHT LINE.<BR>\n" );
document.write( "HENCE ONCE THE LINE IS FIXED BY THE 2 GIVEN POINTS SATISFYING THE GIVEN EQN.ANY OTHER POINT ON THE LINE SHOULD SATISFY THE EQN. AS ELABORATED ABOVE IN THE 4 STIPULATIONS.THAT IS THEY GIVE THE SAME STRAIGHT LINE WHATEVER 2 POINTS YOU TAKE.HENCE ANY 2 POINTS SATISFYING A LINEAR EQN. WILL GIVE YOU THE SAME GRAPH <BR>\n" );
document.write( "FOR THE LINE REPRESENTED BY THE EQN. SINCE <BR>\n" );
document.write( "THE GRAPH IS A STRAIGHT LINE FOR LINEAR EQN. AND ANY 2 POINTS ON THE LINE UNIQUELY DETERMINE THE LINE. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );