document.write( "Question 980315: How to determining at least three points thru which the graph passes?\r
\n" ); document.write( "\n" ); document.write( "1.) x+3=0\r
\n" ); document.write( "\n" ); document.write( "2.) 4x=y+3\r
\n" ); document.write( "\n" ); document.write( "3.) 2y=x-9\r
\n" ); document.write( "\n" ); document.write( "4.) 6x-3y=4\r
\n" ); document.write( "\n" ); document.write( "5.) x=3y \n" ); document.write( "

Algebra.Com's Answer #601627 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
EASIEST WAY:
\n" ); document.write( "Pick a value for $\"x\"$ (or for $\"y\"$ , whichever makes it easier),
\n" ); document.write( "and then find the value of the other variable.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%2B3=0\"$ does not have a $\"y\"$ ,
\n" ); document.write( "and that means that $\"y\"$ can take any value it wants:
\n" ); document.write( " $\"highlight%28y=anything%29\"$ .
\n" ); document.write( "So we solve $\"x%2B3=0\"$ to find the value for $\"x\"$ .
\n" ); document.write( " $\"x%2B3=0\"$ ---> $\"x%2B3-3=0-3\"$ ---> $\"highlight%28x=-3%29\"$ .
\n" ); document.write( "So, your three points could be (-3,0) , (-3,2) , and (-3,4),
\n" ); document.write( "or (-3,-10) , (-3,3) , and (-3,12),
\n" ); document.write( "or any three points with (-3,anything).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For $\"4x=y%2B3\"$ ,
\n" ); document.write( "the easiest way is choosing values for $\"x\"$ ,
\n" ); document.write( "and 0, 1, and 2 are easy numbers to work with.
\n" ); document.write( "Substituting the value $\"x=0\"$ we get
\n" ); document.write( " $\"4%2A0=y%2B3\"$ ---> $\"0=y%2B3\"$ ---> $\"0-3=y%2B3-3\"$ ---> $\"-3=y\"$ ,
\n" ); document.write( "and that gives us the point (0,-3).
\n" ); document.write( "Substituting the value $\"x=1\"$ we get
\n" ); document.write( " $\"4%2A1=y%2B3\"$ ---> $\"4=y%2B3\"$ ---> $\"4-3=y%2B3-3\"$ ---> $\"1=y\"$ ,
\n" ); document.write( "and that gives us the point (1,1).
\n" ); document.write( "Substituting the value $\"x=2\"$ we get
\n" ); document.write( " $\"4%2A2=y%2B3\"$ ---> $\"8=y%2B3\"$ ---> $\"8-3=y%2B3-3\"$ ---> $\"5=y\"$ ,
\n" ); document.write( "and that gives us the point (2,5).\r
\n" ); document.write( "\n" ); document.write( "For $\"+2y=x-9\"$ and $\"x=3y\"$ ,
\n" ); document.write( "I would choose values for $\"y\"$ , because that will make it easier.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For $\"+2y=x-9\"$ , choosing 0, 1, and 2 for $\"y\"$ we get:
\n" ); document.write( "Substituting the value $\"y=0\"$ we get
\n" ); document.write( " $\"2%2A0=x-9\"$ ---> $\"0=x-9\"$ ---> $\"0%2B9=x-9%2B9\"$ ---> $\"9=x\"$ ,
\n" ); document.write( "and that gives us the point (9,0).
\n" ); document.write( "Substituting the value $\"y=1\"$ we get
\n" ); document.write( " $\"2%2A1=x-9\"$ ---> $\"2=x-9\"$ ---> $\"2%2B9=x-9%2B9\"$ ---> $\"11=x\"$ ,
\n" ); document.write( "and that gives us the point (11,1).
\n" ); document.write( "Substituting the value $\"y=2\"$ we get
\n" ); document.write( " $\"2%2A2=x-9\"$ ---> $\"4=x-9\"$ ---> $\"4%2B9=x-9%2B9\"$ ---> $\"13=x\"$ ,
\n" ); document.write( "and that gives us the point (13,2).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For $\"x=3y\"$ , you can figure out what to do.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The graph $\"6x-3y=4\"$ is a bit harder to do,
\n" ); document.write( "because choosing whole number values for one variable gives you fractional values for the other one.
\n" ); document.write( "Sometimes there is nothing better you can do.
\n" ); document.write( "I would make my life easier by choosing
\n" ); document.write( " $\"x=0\"$ for one point,
\n" ); document.write( " $\"y=0\"$ for another point,
\n" ); document.write( "and something else for a third point.
\n" ); document.write( "Substituting the value $\"x=0\"$ we get
\n" ); document.write( " $\"6%2A0-3y=4\"$ ---> $\"0-3y=4\"$ ---> $\"-3y=4\"$ ---> $\"%28-3y%29%2F%28-3%29=4%2F%28-3%29\"$ ---> $\"y=-4%2F3\"$ ,
\n" ); document.write( "and that gives us the point (0,-4/3).
\n" ); document.write( "Substituting the value $\"y=0\"$ we get
\n" ); document.write( " $\"6x-3%2A0=4\"$ ---> $\"6x-0=4\"$ ---> $\"6x=4\"$ ---> $\"6x%2F6=4%2F6\"$ ---> $\"x=2%2F3\"$ ,
\n" ); document.write( "and that gives us the point (2/3,0).
\n" ); document.write( "Then, substituting the value $\"y=2\"$ we get
\n" ); document.write( " $\"6x-3%2A2=4\"$ ---> $\"6x-6=4\"$ ---> $\"6x-6%2B6=4%2B6\"$ ---> $\"6x=10\"$ ---> $\"6x%2F6=10%2F6\"$ ---> $\"x=5%2F3\"$ ,
\n" ); document.write( "and that gives us the point (5/3,2). \n" ); document.write( "

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