Algebra.Com's Answer #366847 by Edwin McCravy(20056)![\"\"](\"/images/stars/stars-13.gif\")  
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What is the equation in slope-intercept form of the line through (1,-3) that is perpendicular to y=5?
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document.write( "y = 5 is the equation of a horizontal line. It should be thought of as\r\n" );
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document.write( "y = 0x + 5\r\n" );
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document.write( "which is an equation in the slope-intercept form:\r\n" );
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document.write( "y = mx + b\r\n" );
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document.write( "So y = 5 is really y = 0x + 5 which has slope 0 and y intercept (0,5).\r\n" );
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document.write( "lines with 0 slope are horizontal since they slope neither uphill to the\r\n" );
document.write( "right (that is, like this /, i.e. have a positive slope) or dwnhill to \r\n" );
document.write( "the right (that is \, i.e., have a negative slope). \r\n" );
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document.write( "Here is the line y = 5 or y = 0x + 5, in green:\r\n" );
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document.write( "Here is the point (1,-3)\r\n" );
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document.write( "Here (in red) is the line through (1,-3) that is perpendicular to the \r\n" );
document.write( "green line, which is the line your problem asks for the equation of.\r\n" );
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document.write( "Notice that the red line you want the equation of is vertical. Vertical \r\n" );
document.write( "lines have no slope. Vertical lines which are parallel to the y-axis can have\r\n" );
document.write( "no y-intercept, since they never intersect it.\r\n" );
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document.write( "The word \"intercept\" in \"slope-intercept form\" refers to the y-intercept\r\n" );
document.write( "only, not the x-intercept. Therefore the red vertical line has no\r\n" );
document.write( "slope-intercept form.\r\n" );
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document.write( "However it DOES have an equation, but not a slope-intercept form.\r\n" );
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document.write( "Its equation is determined by looking at other points on the line,\r\n" );
document.write( "and writing what is true about them. Look at all these other\r\n" );
document.write( "points on that red vertical line?\r\n" );
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document.write( "There is one thing and only one thing that can be said about\r\n" );
document.write( "every one of those points on that red vertical line, and that is:\r\n" );
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document.write( " THEIR x VALUES ARE ALL 1.\r\n" );
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document.write( "Therefore the only equation that describes that vertical line\r\n" );
document.write( "is this simple equation:\r\n" );
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document.write( " x = 1\r\n" );
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document.write( "That is the equation of the red vertical line. However it\r\n" );
document.write( "is NOT a slope-intercept form. Vertical lines are the only\r\n" );
document.write( "kinds of lines that have neither slopes not y-intercepts. The\r\n" );
document.write( "only kinds of equations they can have are this kind:\r\n" );
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document.write( " x = \r\n" );
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document.write( "where there is some number, positive, negative or zero in the box.\r\n" );
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document.write( "Edwin \n" );
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