document.write( "Question 708224: At home sick so I don't have anyone to explain these things to me. How do you find three ordered pairs for the linear equations like x-y=3 or x+7=8 without the constant trial and error I've been doing? I keep trying different numbers but when I get three ordered pairs it doesn't go in an exact line on the graph. \n" ); document.write( "

Algebra.Com's Answer #436046 by KMST(5328) $\"\"$ $\"About$

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$\"x-y=3\"$ is a linear relationship between $\"x\"$ and $\"y\"$ that pairs
\n" ); document.write( "each value of $\"x\"$ with just one value of $\"y\"$ , and
\n" ); document.write( "each value of $\"y\"$ with just one value of $\"x\"$ .
\n" ); document.write( "To find one pair, you assign a value to one variable (the $\"x\"$ or the $\"y\"$ ) and
\n" ); document.write( "solve to find the corresponding value of the other variable.
\n" ); document.write( "Choosing zero usually works well.
\n" ); document.write( "For $\"x=0\"$ the equation turns into $\"0-y=3\"$ or $\"-y=3\"$ , so $\"y=-3\"$ and you have the pair (0,-3).
\n" ); document.write( "For $\"y=0\"$ the equation turns into $\"x-0=3\"$ , so $\"x=3\"$ and you have the pair (3,0).
\n" ); document.write( "For a third pair, you can chose any number that works for you.
\n" ); document.write( "If all you need is a pair, the choice is easier.
\n" ); document.write( "In this case, you could chose $\"y=2\"$ --> $\"x-2=3\"$ --> $\"x=3%2B2\"$ --> $\"x=5\"$ and would have (5,2) for the third point.
\n" ); document.write( "If you want to use points to graph the line, it may get trickier,
\n" ); document.write( "but if your first choice does not work well for graphing, you can try again.
\n" ); document.write( "
\n" ); document.write( " $\"x%2B7=8\"$ would just give you a value for x, but no value for y.
\n" ); document.write( "There is no one-to-to one relationship between between $\"x\"$ and $\"y\"$ there.
\n" ); document.write( "The equation $\"x%2B7=8\"$ is the equation of a \"vertical\" line,
\n" ); document.write( "made of all the points that have
\n" ); document.write( " $\"x=8-7\"$ --> $\"x=1\"$ and $\"y=any\"$ $\"number\"$
\n" ); document.write( "Your choices for points are as infinite as with any line,
\n" ); document.write( "but they are also infinitely easy:
\n" ); document.write( "(1,-5), (1,0), (1,3), (1,5.5), or (1,anything).
\n" ); document.write( "
\n" ); document.write( "You may have meant meant $\"x%2B7y=8\"$ . If so, just try the same strategies that I described for the other equation.
\n" ); document.write( " $\"x=0\"$ --> $\"7y=8\"$ --> $\"y=8%2F7\"$ may not look good to you,
\n" ); document.write( "but giving values to $\"y\"$ may be more to your liking.
\n" ); document.write( " $\"y=0\"$ --> $\"x=8\"$ gives you point (8,0)
\n" ); document.write( " $\"y=1\"$ --> $\"x-7=8\"$ --> $\"x=8%2B7\"$ --> $\"x=15\"$ gives you (15,1).
\n" ); document.write( " $\"y=2\"$ --> $\"x-14=8\"$ --> $\"x=8%2B14\"$ --> $\"x=22\"$ gives you (22,1).
\n" ); document.write( " $\"y=-1\"$ --> $\"x-7%28-1%29=8\"$ --> $\"x%2B7=8\"$ --> $\"x=8-7\"$ --> $\"x=1\"$ gives you (1,-1). \n" ); document.write( "

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