document.write( "Question 366966: complete a t-chart and graph: 4x + 3 = 8y \n" ); document.write( "
Algebra.Com's Answer #261631 by Edwin McCravy(20055) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "Swap sides:\r\n" );
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document.write( "Divide both sides by 8 to solve for y\r\n" );
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document.write( "It is not possible to get whole numbers for y using whole\r\n" );
document.write( "numbers for x, because the numerator will always be odd,\r\n" );
document.write( "since it's an even number (4x) plus an odd number (3) and\r\n" );
document.write( "therefore it can never be divisible by 8.\r\n" );
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document.write( "So we have no choice but to put up with fractions.\r\n" );
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document.write( "We make a t-chart.  I arbitrarily choose 5 for x\r\n" );
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document.write( " x | y\r\n" );
document.write( " 5 |\r\n" );
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document.write( "Now I substitute 5 for x in the equation: \r\n" );
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document.write( "Fraction numbers are easier to plot when expressed as a decimal:\r\n" );
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document.write( " x | y\r\n" );
document.write( " 5 | 2.875\r\n" );
document.write( "   |\r\n" );
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document.write( "The point (5,2.875) is between the points (5,2) and (5,3), a little\r\n" );
document.write( "bit below (5,3) because 2.875 is a tiny bit below (5,3).  I'll draw \r\n" );
document.write( "(5,2) and (5,3) in green and the point (5,2.875) in black:\r\n" );
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document.write( "   \r\n" );
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document.write( "Now I'll take the green points away.  I just put them there to\r\n" );
document.write( "show you that you just have to guess where points with fraction\r\n" );
document.write( "coordinates are located, as they are in between the points with whole \r\n" );
document.write( "number coordinates.\r\n" );
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document.write( "-----\r\n" );
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document.write( "Now I arbitrarily choose another value for x, say -4\r\n" );
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document.write( " x | y\r\n" );
document.write( " 5 | 2.875\r\n" );
document.write( "-4 |\r\n" );
document.write( "   |\r\n" );
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document.write( "Now I substitute 5 for x in the equation: \r\n" );
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document.write( "Fraction numbers are easier to plot when expressed as a decimal:\r\n" );
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document.write( " x | y\r\n" );
document.write( " 5 | 2.875\r\n" );
document.write( "-4 |-1.625 \r\n" );
document.write( "   |\r\n" );
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document.write( "To plot (-4,-1.625) is between the points (-4,1) and (-4,2), a little\r\n" );
document.write( "bit closer to (-4,2) because .625 is a little more than halfway between\r\n" );
document.write( "them, which would be (-4,-1.5).  I'll draw (-4,-1) and (-4,-2) in green and the point (-4,-1.625) in black:\r\n" );
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document.write( "   \r\n" );
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document.write( "Now I'll take the green points away.  As before, I just put them \r\n" );
document.write( "there to show you that you just have to guess where points with fraction\r\n" );
document.write( "coordinates are located, as they are in between the points with whole \r\n" );
document.write( "number coordinates.\r\n" );
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document.write( "Now I could draw a line through them.  However in case I made a mistake\r\n" );
document.write( "I should plot a third point as a check.  Then if it doesn't line up with the\r\n" );
document.write( "other two so that I cannot draw a line through all three points, then I'll know\r\n" );
document.write( "I made an error somewhere.  If it lines up so that I can draw a line through\r\n" );
document.write( "all three points, then I'll know I'm right. \r\n" );
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document.write( "So I arbitrarily choose a third value for x as a check, say 1\r\n" );
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document.write( " x | y\r\n" );
document.write( " 5 | 2.875\r\n" );
document.write( "-4 |-1.625 \r\n" );
document.write( " 1 | \r\n" );
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document.write( "Now I substitute 1 for x in the equation: \r\n" );
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document.write( "Fraction numbers are easier to plot when expressed as a decimal:\r\n" );
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document.write( "\r\n" );
document.write( " x | y\r\n" );
document.write( " 5 | 2.875\r\n" );
document.write( "-4 |-1.625 \r\n" );
document.write( " 1 |  .875\r\n" );
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document.write( "The point (1,.875) is between the points (1,0) and (1,1), a little\r\n" );
document.write( "bit below (1,1) because .875 is a tiny bit below (1,1).  I'll draw \r\n" );
document.write( "(1,0) and (1,1) in green and the point (1,.875) in black:\r\n" );
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document.write( "   \r\n" );
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document.write( "Now I'll take the green points away.  As before, I just put them \r\n" );
document.write( "there to show you that you just have to guess where points with fraction\r\n" );
document.write( "coordinates are located, as they are in between the points with whole \r\n" );
document.write( "number coordinates.\r\n" );
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document.write( "Now let's see if we can draw a line through all three\r\n" );
document.write( "points. If I can I'll draw it in blue:\r\n" );
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document.write( "Edwin
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