document.write( "Question 100763: A temperature of 10°C corresponds to a temperature of 50°F. Also 40°C corresponds to 104°F. Find the linear equation relating F and C. \n" ); document.write( "

Algebra.Com's Answer #73371 by oberobic(2304) $\"\"$ $\"About$

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We are given:
\n" ); document.write( " $\"10C+=+50F\"$
\n" ); document.write( " $\"40C+=+104F\"$
\n" ); document.write( "We can assume we have a grid of C (the x-axis) and F (the y-axis).
\n" ); document.write( "So these correspondences can be viewed as xy pairs that define points in the plane: (10,50) and (40,104).
\n" ); document.write( "Finding the slope of the line, we have:
\n" ); document.write( "

\n" ); document.write( "The general equation for a line is y = mx + b, so
\n" ); document.write( " $\"y+=+%289%2F5%29x+%2B+b\"$
\n" ); document.write( "And, looking back we notice that when x=10, y=50. So we can substitute:
\n" ); document.write( " $\"50+=+%289%2F5%2910+%2B+b\"$
\n" ); document.write( " $\"50+=+18+%2B+b\"$ , so
\n" ); document.write( " $\"b+=+32\"$ , which is the y-intercept.
\n" ); document.write( "Now the equation is
\n" ); document.write( " $\"y+=+%289%2F5%29x+%2B+32\"$ , which is perhaps more familiar by substituting F for y (meaning degrees Farenheit) and C for x (meaning Celsius).
\n" ); document.write( " $\"F+=+%289%2F5%29C+%2B+32\"$ . \n" ); document.write( "

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