document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181340>Question 1181340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> As the number of units manufactured increased from 100 to 200, manufacturing cost (total) <BR>\n" );
document.write( "increased from $350 to $650. Assume the given data establish the relationship between cost (y) <BR>\n" );
document.write( "and number of units made (x), and assume the relationship is linear. Find the equation of the <BR>\n" );
document.write( "relationship </SPAN>\n" );
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document.write( "A linear equation is of the form<br><BR>\n" );
document.write( "y = mx+b<br><BR>\n" );
document.write( "where m is the slope (rate of change of y with respect to x) and b is the value when x is 0.<br><BR>\n" );
document.write( "With the given information, the cost increased by $650-$350=$300 when the number of units produced increased by 200-100=100.  So the rate of change of cost (y) with respect to x (number of units) is 300/100=3.<br><BR>\n" );
document.write( "So the equation is of the form<br><BR>\n" );
document.write( "y = 3x+b<br><BR>\n" );
document.write( "Use one of the two given data points to determine b.<br><BR>\n" );
document.write( "When production was 100, the total cost was $350:<br><BR>\n" );
document.write( "350 = 3(100)+b<BR>\n" );
document.write( "350 = 300+b<BR>\n" );
document.write( "b = 50<br><BR>\n" );
document.write( "ANSWER: y=3x+50 is the linear equation relating the total cost to the number of units produced.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );