document.write( "Question 1036485: find linear function f given f(2)=3 and f(6)=4
\n" ); document.write( "Im lost not how to do \n" ); document.write( "

Algebra.Com's Answer #651176 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the general form of the linear
\n" ); document.write( "equation be:
\n" ); document.write( " $\"+f%28x%29+=+a%2Ax+%2B+b+\"$
\n" ); document.write( "----------------
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+f%282%29+=+a%2A2+%2B+b+\"$
\n" ); document.write( "(2) $\"+f%286%29+=+a%2A6+%2B+b+\"$
\n" ); document.write( "------------------
\n" ); document.write( "Also given:
\n" ); document.write( " $\"+f%282%29+=+3+\"$
\n" ); document.write( "(1) $\"+3+=+a%2A2+%2B+b+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+f%286%29+=+4+\"$
\n" ); document.write( "(2) $\"+4+=+a%2A6+%2B+b+\"$
\n" ); document.write( "------------------
\n" ); document.write( "Rewrite (1) and (2)
\n" ); document.write( "(1) $\"+2a+%2B+b+=+3+\"$
\n" ); document.write( "(2) $\"+6a+%2B+b+=+4+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "subtract (1) from (2)
\n" ); document.write( "(2) $\"+6a+%2B+b+=+4+\"$
\n" ); document.write( "(1) $\"+-2a+-+b+=+-3+\"$
\n" ); document.write( "-------------------
\n" ); document.write( " $\"+4a+=+1+\"$
\n" ); document.write( " $\"+a+=+1%2F4+\"$
\n" ); document.write( "-------------
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+2%2A%281%2F4%29+%2B+b+=+3+\"$
\n" ); document.write( "(1) $\"+1%2F2+%2B+b+=+3+\"$
\n" ); document.write( "(1) $\"+1+%2B+2b+=+6+\"$
\n" ); document.write( "(1) $\"+2b+=+5+\"$
\n" ); document.write( "(1) $\"+b+=+5%2F2+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "So, the linear equation is:
\n" ); document.write( " $\"+f%28x%29+=+%281%2F4%29%2Ax+%2B+5%2F2+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+f%282%29+=+3+\"$
\n" ); document.write( " $\"+x+=+2+\"$
\n" ); document.write( " $\"+%281%2F4%29%2A2+%2B+5%2F2+=+3+\"$
\n" ); document.write( " $\"+1%2F2+%2B+5%2F2+=+3+\"$
\n" ); document.write( " $\"+6%2F2+=+3+\"$
\n" ); document.write( " $\"+3+=+3+\"$
\n" ); document.write( "----------------------
\n" ); document.write( " $\"+f%286%29+=+4+\"$
\n" ); document.write( " $\"+x+=+6+\"$
\n" ); document.write( " $\"+%281%2F4%29%2A6+%2B+5%2F2+=+4+\"$
\n" ); document.write( " $\"+3%2F2+%2B+5%2F2+=+4+\"$
\n" ); document.write( " $\"+8%2F2+=+4+\"$
\n" ); document.write( " $\"+4+=+4+\"$
\n" ); document.write( "OK \n" ); document.write( "

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