document.write( "Question 178719: What is the equation for the function in the form f(x)= mx+b?
\n" ); document.write( "f(1)=1, f(4)=10\r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "

Algebra.Com's Answer #133686 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"y\"$ is a function of $\"x\"$ , or
\n" ); document.write( " $\"y+=+f%28x%29\"$
\n" ); document.write( "given:
\n" ); document.write( " $\"1+=+f%281%29\"$
\n" ); document.write( " $\"y+=+1\"$
\n" ); document.write( " $\"x+=+1\"$
\n" ); document.write( "This gives me the point (1,1)
\n" ); document.write( " $\"10+=+f%284%29\"$
\n" ); document.write( " $\"y+=+10\"$
\n" ); document.write( " $\"x+=+4\"$
\n" ); document.write( "This gives me the point (4,10)
\n" ); document.write( " $\"f%28x%29+=+mx+%2B+b\"$
\n" ); document.write( " $\"y+=+f%28x%29\"$
\n" ); document.write( " $\"y+=+mx+%2B+b\"$
\n" ); document.write( "For the point (1,1):
\n" ); document.write( "(1) $\"1+=+m%2A1+%2B+b\"$
\n" ); document.write( "For the point (4,10):
\n" ); document.write( "(2) $\"10+=+m%2A4+%2B+b\"$
\n" ); document.write( "Multiply (1) by $\"4\"$ and subtract from (2)
\n" ); document.write( "(2) $\"10+=+4m+%2B+b\"$
\n" ); document.write( "(1) $\"-4+=+-4m+-+4b\"$
\n" ); document.write( " $\"6+=+-3b\"$
\n" ); document.write( " $\"b+=+-2\"$
\n" ); document.write( "Substitute this in (1)
\n" ); document.write( "(1) $\"1+=+m%2A1+%2B+b\"$
\n" ); document.write( " $\"1+=+m+-+2\"$
\n" ); document.write( " $\"m+=+3\"$
\n" ); document.write( "The equation is $\"f%28x%29+=+3x+-+2\"$ answer \r
\n" ); document.write( "\n" ); document.write( "check:
\n" ); document.write( "does it go through (1,1)?
\n" ); document.write( " $\"1+=+3%2A1+-+2\"$
\n" ); document.write( " $\"1+=+1\"$
\n" ); document.write( "OK
\n" ); document.write( "Does it go through (4,10)?
\n" ); document.write( " $\"10+=+3%2A4+-+2\"$
\n" ); document.write( " $\"10+=+10\"$
\n" ); document.write( "OK \n" ); document.write( "

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