document.write( "Question 508739: Can you help me write each linear in slope-intercept form then graph the inequality 2x-3y>7 \n" ); document.write( "

Algebra.Com's Answer #341103 by Edwin McCravy(20055) $\"\"$ $\"About$

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Can you help me write each linear in slope-intercept form then graph the inequality 2x - 3y > 7
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document.write( "In order to graph an inequality we first have to draw the graph of \r\n" );
document.write( "the boundary, which is the equation formed by replacing the inequality\r\n" );
document.write( "sign > by =\r\n" );
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document.write( "First we draw the graph of \r\n" );
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document.write( "2x - 3y = 7\r\n" );
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document.write( "We put it in slope intercept form:\r\n" );
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document.write( "Add -2x to both sides:\r\n" );
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document.write( "   -3y = -2x + 7\r\n" );
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document.write( "Divide every number by -3\r\n" );
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document.write( " y = x + \r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "     y = x - \r\n" );
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document.write( "The y-intercept is at  on the y-axis, the slope is \r\n" );
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document.write( "So we start at the y-intercept (0,) or (0,),\r\n" );
document.write( "See the little dot about 1/3 of the way from -2 toward -3:\r\n" );
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document.write( "Then we notice that the numerator of the slope is 2, so we draw a line\r\n" );
document.write( "from the y-intercept 2 units upward:\r\n" );
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document.write( "Then we notice that the denominator of the slope is 3, so from the end\r\n" );
document.write( "of that line (where the arrowhead is) we draw another line 3 units to\r\n" );
document.write( "the right:\r\n" );
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document.write( "Next we draw the boundary line through the y-intercept and the second arrowhead.\r\n" );
document.write( "We draw it as a dotted line because the inequality is > and not >. The\r\n" );
document.write( "solution does not include the boundary line.\r\n" );
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document.write( "Next we must find out whether we are to shade the region above the dotted \r\n" );
document.write( "boundary line, or the region below it.\r\n" );
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document.write( "So we choose any arbitrary TEST POINT that does not lie on the dotted \r\n" );
document.write( "boundary line, say the point (x,y) = (2,3)\r\n" );
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document.write( "and substitute it into the original\r\n" );
document.write( "inequality:\r\n" );
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document.write( "    2x - 3y > 7\r\n" );
document.write( "2(2) - 3(3) > 7\r\n" );
document.write( "      4 - 9 > 7\r\n" );
document.write( "         -5 > 7\r\n" );
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document.write( "That is false, so (2,3) is NOT a solution, so that means that the \r\n" );
document.write( "solutions are NOT on the upper side of the boundary line so we \r\n" );
document.write( "shade the lower side of the line, like this:\r\n" );
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document.write( "That bright red shaded area is the graph of the inequality.\r\n" );
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document.write( "Edwin

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