document.write( "Question 1144140: Find an equation of the line in the form ax+by=c, where a, b, and c are integers with no factor common to all three and a>=0.
\n" ); document.write( "The line with y-intercept 9 and perpendicular to x+5y=19 \n" ); document.write( "

Algebra.Com's Answer #765145 by ikleyn(52817) $\"\"$ $\"About$

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document.write( "There is a standard procedure on how to construct an equation of a line perpendicular to a given line.\r\n" );
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document.write( "    This procedure is described in all details with examples in my lesson\r\n" );
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document.write( "        - Equation for a straight line perpendicular to a given line and passing through a given point \r\n" );
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document.write( "    in this site, which I recommend you to read and to learn.\r\n" );
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document.write( "In this case this procedure works in this way:\r\n" );
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document.write( "    a)  take the form  \"x + 5y\" of the given equation of the given line.\r\n" );
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document.write( "    b)  in this form, swap the coefficients and change the sign at one of the coefficient, keeping the other coefficient with its original sign.\r\n" );
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document.write( "    c)  By doing in this way, yo will get the left side of the projected equation in the form\r\n" );
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document.write( "           \"5x - y\",\r\n" );
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document.write( "        so the future equation will take the form  \r\n" );
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document.write( "            5x - y = c,      (1)\r\n" );
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document.write( "        where \" c \" is some constant, now unknown.\r\n" );
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document.write( "    d)  To determine the constant \" c \" value, use the fact the the projected line passes through the point (x,y) = (0,9)\r\n" );
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document.write( "         and substitute these coordinates into equation (1).  It will give you\r\n" );
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document.write( "             c = 5x - y = 5*0 - 9 = -9.\r\n" );
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document.write( "    e)  Thus the final equation of the perpendicular line is\r\n" );
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document.write( "              5x - y = -9.\r\n" );
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document.write( "        It satisfies all requirements of the problem.\r\n" );
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