document.write( "Question 1101807: The line ax+by-5=0 passes through the point (-2,8) and is perpendicular to the line 2x-5y+5=0. Find the value of a and b. \n" ); document.write( "

Algebra.Com's Answer #716432 by ikleyn(52914) $\"\"$ $\"About$

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document.write( "The line perpendicular to the line 2x - 5y + 5 = 0 is the line of the form\r\n" );
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document.write( "5x + 2y = c,         (1)\r\n" );
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document.write( "where \"c\" is some constant which must be determined from the other condition,\r\n" );
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document.write( "         OR ANY OTHER EQUATION EQUIVALENT TO eq(1).\r\n" );
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document.write( "This other condition for \"c\" is \"the line (1) passes through the point (-2,8).\"\r\n" );
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document.write( "Therefore, we can determine \"c\" from the equation (1) by substituting x= -2  and  y= 8 into equation (1).  By doing so, you will get\r\n" );
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document.write( "5*(-2) + 2*8 = c = -10+16 = 6.\r\n" );
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document.write( "So, the equation of the line (1) is \r\n" );
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document.write( "5x + 2y = 6,   or\r\n" );
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document.write( "5x + 2y - 6 = 0.      (2)\r\n" );
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document.write( "Now multiply eq(2) by  (both sides).  You will get an equivalent equation \r\n" );
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document.write( " = 0.   (3).\r\n" );
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document.write( "Now comparing the equation (3) with the equation ax + by - 5 = 0,  \r\n" );
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document.write( "you can conclude that  a =    and  b = .\r\n" );
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