document.write( "Question 1107802: how to solve for slope without using derivatives? please help :(
\n" ); document.write( "y=-8/√x at points (4, -4) \n" ); document.write( "

Algebra.Com's Answer #722837 by ikleyn(52780) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Consider the system of 2 equations \r\n" );
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document.write( "y = ,              (1)\r\n" );
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document.write( "y - (-4) = m(x-4).       (2)\r\n" );
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document.write( "It is the same, as the system\r\n" );
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document.write( "y = ,              (1)\r\n" );
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document.write( "y + 4 = m(x-4).          (2)\r\n" );
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document.write( "Find  the slope \"m\" under the condition that the system has a UNIQUE solution (x,y) = (4,-4).\r\n" );
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document.write( "For it, substitute expression for y,  y = m*(x-4)-4  into equation (1). You will get\r\n" );
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document.write( "m*(x-4) + 4 = .       (*)\r\n" );
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document.write( "Introduce new variable  u = .  Then the equation (*) takes the form\r\n" );
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document.write( " = ,\r\n" );
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document.write( " = ,\r\n" );
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document.write( " = 0.             (**)\r\n" );
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document.write( "The condition that the equation (**) has a unique solution in \"u\"  means that the discriminant of the equation (**) is equal to zero.\r\n" );
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document.write( "Write the discriminant of the quadratic equation (**) and equate it to zero:\r\n" );
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document.write( "d =  =  = 16 - 16m  ====>\r\n" );
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document.write( "the equation d = 0  becomes  16 - 16m = 0,  which implies  16m = 16  ====>  m = 1.\r\n" );
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document.write( "Answer.  The slope under the question is  m= 1,\r\n" );
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document.write( "         found without using derivatives.\r\n" );
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