document.write( "Question 1161245: Use the slope and y-intercept to graph the following system of equations. State the solution to the system of equations. y = 1/2x - 6 and -2x - y = -9. \n" ); document.write( "
Algebra.Com's Answer #784750 by Edwin McCravy(20056) $\"\"$ $\"About$
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document.write( "First get it in the form y = mx + b  if it's not already in that form.\r\n" );
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document.write( "That's already in the form y = mx + b, \r\n" );
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document.write( "The \"b\", which reminds us of the word \"begin\" is -6.\r\n" );
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document.write( "That tells us where to begin on the y-axis:\r\n" );
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document.write( "So we put our pencil at -6 on the y-axis, where the\r\n" );
document.write( "dot is below\r\n" );
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document.write( "The \"m\", which reminds us of the word \"move\" is 1/2, which is the slope.\r\n" );
document.write( "Its numerator tells us how many units to go up or down.  If it's a\r\n" );
document.write( "psitive number, numerator tells us how many its to go up, and if it's\r\n" );
document.write( "a negative number it tells us how many units to go down.  Since 1/2 is\r\n" );
document.write( "a positive number, we go up the numerator number of units, which is up\r\n" );
document.write( "1 unit, so we draw a line from that point we drew upward 1 unit. See the\r\n" );
document.write( "green line drawn upward 1 unit below \r\n" );
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document.write( "The denominator tells us how many units to go right.  We ALWAYS go right\r\n" );
document.write( "with the denominator.  The denominator of m is 2 so we go right the\r\n" );
document.write( "denominator number of units, so we draw a line from that point we drew\r\n" );
document.write( "rightward 2 units. See the horizontal green line drawn rightward 2 units\r\n" );
document.write( "below:\r\n" );
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document.write( "Now take a ruler and draw the line which the equation represents.  The\r\n" );
document.write( "line goes through the first point we drew and goes through the end point\r\n" );
document.write( "of the green horizontal line.  Like this:\r\n" );
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document.write( "But the second one, -2x - y = -9, is not in the form y = mx + b\r\n" );
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document.write( "Here is how we get it in that form:\r\n" );
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document.write( "                    -2x - y =    - 9\r\n" );
document.write( "                    +2x      +2x\r\n" );
document.write( "                  -------------------\r\n" );
document.write( "                         -y = 2x - 9 \r\n" );
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document.write( " Divide every term by -1\r\n" );
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document.write( "                        -y  = 2x -  9\r\n" );
document.write( "                        ———   ——   ———\r\n" );
document.write( "                        -1    -1   -1\r\n" );
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document.write( "                         y  = -2x + 9\r\n" );
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document.write( "Now we have to consider m=-2 as the fraction m=-2/1\r\n" );
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document.write( "---\r\n" );
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document.write( "The \"b\", which reminds us of the word \"begin\" is 9.\r\n" );
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document.write( "That tells us where to begin on the y-axis:\r\n" );
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document.write( "So we put our pencil at 9 on the y-axis, where the\r\n" );
document.write( "dot is below\r\n" );
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document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The \"m\", which reminds us of the word \"move\" is -2/1, which is the slope.\r\n" );
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document.write( "Its numerator tells us how many units to go up or down.  If it's a\r\n" );
document.write( "positive number, numerator tells us how many its to go up, and if it's\r\n" );
document.write( "a negative number it tells us how many units to go down.  Since -2/1 is\r\n" );
document.write( "a negative number, we go down the numerator number of units, which is down\r\n" );
document.write( "2 units, so we draw a line from that point we drew downward 2 units. See the\r\n" );
document.write( "green line drawn downward 2 units below: \r\n" );
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document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The denominator tells us how many units to go right.  We ALWAYS go right\r\n" );
document.write( "with the denominator.  The denominator of m is 1 so we go right the\r\n" );
document.write( "denominator number of units, so we draw a line from that point we drew\r\n" );
document.write( "rightward 1 units. See the horizontal green line drawn rightward 1 units\r\n" );
document.write( "below:\r\n" );
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document.write( " \r\n" );
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document.write( "Now take a ruler and draw the line which the equation represents.  The\r\n" );
document.write( "line goes through the first point we drew and goes through the end point\r\n" );
document.write( "of the green horizontal line.  Like this:\r\n" );
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document.write( "Edwin
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