document.write( "Question 306748: Suppose line l contains the points (5, 6) and (4, 3). Determine the equation of the line that:\r
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Algebra.Com's Answer #219467 by Edwin McCravy(20055) $\"\"$ $\"About$

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Suppose line l contains the points (5, 6) and (4, 3). Determine the equation of the line that:
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document.write( "The other tutor's solution is a different problem:\r\n" );
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document.write( "Here are those points plotted:\r\n" );
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document.write( "Now we get a ruler and draw a green line through them:\r\n" );
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document.write( "We find the equation of that green line that contains the points\r\n" );
document.write( "(5, 6) and (4, 3) by using the slope formula\r\n" );
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document.write( "Now we use the point-slope form:\r\n" );
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document.write( "Now we simplify it to get the slope-y-intercept form\r\n" );
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document.write( "Comparing it to the slope-y-intercept form\r\n" );
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document.write( ", whose slope is m and whose y-intercept is (0,b)\r\n" );
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document.write( "We find that its y-intercept is (0,-9).\r\n" );
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document.write( "We can see in the graph above that the green line appears to \r\n" );
document.write( "have that y-intercept.\r\n" );
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document.write( "Now we want the equation of another line which is perpendicular\r\n" );
document.write( "to that line.  It's slope will be the reciprocal of the slope 3\r\n" );
document.write( "with the sign changed.  That is, the slope of the required line\r\n" );
document.write( "will have slope .\r\n" );
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document.write( "This required line is to have the same y-intercept (0.-9), that\r\n" );
document.write( "the given line has.\r\n" );
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document.write( "so its equation is\r\n" );
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document.write( "We already have one point on the required line, the y-intercept\r\n" );
document.write( "(0,-9). We'll find another point on it, say, by substituting \r\n" );
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document.write( "So we see that the required line goes through (-3,-8) and (0,-9)\r\n" );
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document.write( "Getting our ruler again, and drawing a blue line through (0,-9) and\r\n" );
document.write( "(-3,-8) we have:\r\n" );
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document.write( "The blue line looks very much perpendicular to the green line\r\n" );
document.write( "and so we are satisfied that \r\n" );
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document.write( "is the required equation of the required line. \r\n" );
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document.write( "If you like you can put it in general form by multiplying through by 3,\r\n" );
document.write( "then adding x to both sides:\r\n" );
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document.write( "Edwin

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