document.write( "Question 159464: Give the equation of the linear function, f(x) if f(1) = 4 and f(3) = 8 \n" ); document.write( "

Algebra.Com's Answer #117653 by Fombitz(32388) $\"\"$ $\"About$

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A linear equation has the form,
\n" ); document.write( " $\"f%28x%29=mx%2Bb\"$
\n" ); document.write( "Let's use the values you provide and solve for m and b.
\n" ); document.write( "First value,
\n" ); document.write( " $\"f%28x%29=mx%2Bb\"$
\n" ); document.write( " $\"4=m%281%29%2Bb\"$
\n" ); document.write( "1. $\"m%2Bb=4\"$
\n" ); document.write( "Second value,
\n" ); document.write( " $\"f%28x%29=mx%2Bb\"$
\n" ); document.write( " $\"8=m%283%29%2Bb\"$
\n" ); document.write( "2. $\"3m%2Bb=8\"$
\n" ); document.write( "Subtract eq. 1 from eq. 2,
\n" ); document.write( " $\"3m%2Bb-%28m%2Bb%29=8-4\"$
\n" ); document.write( " $\"2m=4\"$
\n" ); document.write( " $\"m=2\"$
\n" ); document.write( "From eq. 1,
\n" ); document.write( "1. $\"m%2Bb=4\"$
\n" ); document.write( " $\"2%2Bb=4\"$
\n" ); document.write( " $\"b=2\"$
\n" ); document.write( "The linear equation is,
\n" ); document.write( " $\"f%28x%29=2x%2B2\"$ \n" ); document.write( "

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