document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171005>Question 1171005</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $88 for 180 miles. On another day she rented a car from the same agency and paid $151 for 360 miles. Find the linear function f(x) (where x is in miles and f(x) is in dollars) that the agency could use to determine its daily rental charges </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795935 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=795935\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general form of the linear equation is y = mx + b<BR>\n" );
document.write( "y is the total cost.<BR>\n" );
document.write( "x is the number of miles driven.<BR>\n" );
document.write( "m is the slope.<BR>\n" );
document.write( "b is the y-intercept.<BR>\n" );
document.write( "the y-intercept is the value of y when the value of x is equal to 0.<BR>\n" );
document.write( "the slope is equal to (y2 - y1) / (x2 - x1).<BR>\n" );
document.write( "(x1,y1) and (x2,y2) are data points on the line of the equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have two data points to work with.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "(180,88)<BR>\n" );
document.write( "(360,151)<BR>\n" );
document.write( "these are in (x,y) format.<BR>\n" );
document.write( "for example, (180,88) means y = 88 when x = 180.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "assign one of these points to (x1,y1) and assign the other point to (x2,y2)<BR>\n" );
document.write( "i assigned (180,88) to (x1,y1) and (360,151) to (x2,y2).<BR>\n" );
document.write( "m = slope = (y2-y1)/(x2-x1) = (151-88) / (360-180) = 63 / 180 = .35<BR>\n" );
document.write( "y = mx + b becomes y = .35 * x + b\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to find the value of b, replace x and y with the value from one of the points.<BR>\n" );
document.write( "i chose (360,151).<BR>\n" );
document.write( "y = .35 * x + b becomes 151 = .35 * 360 + b<BR>\n" );
document.write( "solve for b to get:<BR>\n" );
document.write( "b = 151 - .35 * 360 = 25<BR>\n" );
document.write( "y = .35 * x + b becomes y = .35 * x + 25\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equation is y = .35 * x + 25.<BR>\n" );
document.write( "when x = 0, you get y = 25<BR>\n" );
document.write( "when x = 180, you get y = .35 * 180 + 25 = 88.<BR>\n" );
document.write( "when x = 360, you get y = .35 * 360 + 25 = 151<BR>\n" );
document.write( "the equation is confirmed to be good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your solution is that the linear equation used to determine its daily rental charges is y = .35 * x + 25.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );