document.write( "Question 1036056: If f(x) is a linear function such that f(2) ≤ f(3), f(4) ≥ f(5), and f(6)=10.
\n" ); document.write( "Prove that line \"f\" is a flat line. \n" ); document.write( "

Algebra.Com's Answer #650638 by robertb(5830) $\"\"$ $\"About$

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f(x) a linear function implies that f(x) = ax + b for some constants a and b.
\n" ); document.write( "Note that a is the slope of the line and b is the y-intercept of the line.\r
\n" ); document.write( "\n" ); document.write( "Now $\"f%282%29+=+2a+%2B+b+%3C=+3a+%2B+b+=+f%283%29\"$ ==> $\"0+%3C=+a\"$ . \r
\n" ); document.write( "\n" ); document.write( "Also,\r
\n" ); document.write( "\n" ); document.write( " $\"f%284%29+=+4a+%2B+b+%3E=+5a+%2B+b+=+f%285%29\"$ ==> $\"0+%3E=+a\"$ . \r
\n" ); document.write( "\n" ); document.write( "Hence $\"0+%3C=+a\"$ and $\"0+%3E=+a\"$ ==> a = 0 ==> line has slope 0, and thus it is a horizontal line, or a \"flat\" line.\r
\n" ); document.write( "\n" ); document.write( "==> f(x) = b, and since f(6) = 10 = b, the linear function is $\"highlight%28f%28x%29+=+10%29\"$ . \n" ); document.write( "

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