document.write( "Question 1101811: 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 #716434 by ikleyn(52782) $\"\"$ $\"About$

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\n" ); document.write( "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.
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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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\n" ); document.write( "comment from student: Hi! Thanks for helping me but can you please explain to me how 5x - 2y = c is perpendicular 2x - 5y + 5 = 0. Thank you!
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\n" ); document.write( "\n" ); document.write( "My response: \r
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\n" ); document.write( "\n" ); document.write( "Let me first TO CORRECT your question. It should be
\n" ); document.write( "\"can you please explain to me how 5x+2y=0 is perpendicular 2x-5y+5=0 ?\" \r
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document.write( "5x + 2y = c      has the slope .\r\n" );
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document.write( "2x - 5y + 5 = 0  has the slope  \r\n" );
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document.write( "The two slopes are reciprocal and have opposite signs !!\r\n" );
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