document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104227>Question 1104227</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The volume of gas in your car’s gas tank depends on the number of miles you have driven. <BR>\n" );
document.write( "Suppose you leave home with a full tank and begin driving at a constant speed. After driving 120 miles you have 12 gallons in your tank. <BR>\n" );
document.write( "After driving 220 miles you have 8.66 gallons in your tank. <BR>\n" );
document.write( "Assume the relationship is linear. \r<BR>\n" );
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document.write( "a. Find a function that models this situation.  (Input miles driven and output gallons of gas in your tank.)\r<BR>\n" );
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document.write( "b. How many gallons does your gas tank hold when full?\r<BR>\n" );
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document.write( "c. How many miles can you drive before you will run out of gas?\r<BR>\n" );
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document.write( "d. What is your car's approximate fuel efficiency in miles per gallon?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #718966 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=718966\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x equal your miles.<BR>\n" );
document.write( "let y equal the number of gallons of gas.\r<BR>\n" );
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document.write( "it's a linear relationship.<BR>\n" );
document.write( "the slope intercept form of a linear equation is y = mx + b<BR>\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept.\r<BR>\n" );
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document.write( "you have 2 coordinates you can work with.<BR>\n" );
document.write( "they are (120,12) and (220,8.66)\r<BR>\n" );
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document.write( "let the first one be (x1,y1).<BR>\n" );
document.write( "let the second one be (x2,y2).\r<BR>\n" );
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document.write( "m = slope = (y2-y1) / (x2-x1) = (8.66-12)) / (220-120) = -.0334<BR>\n" );
document.write( "equation of y = mx + b becomes y = -.0334 * x + b\r<BR>\n" );
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document.write( "use either one of the points to find the y-intercept.<BR>\n" );
document.write( "i'll use (120,12).<BR>\n" );
document.write( "replace y with 12 and x with 120 to get 12 = -.0334 * 120 + b<BR>\n" );
document.write( "solve for b to get b = 16.008\r<BR>\n" );
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document.write( "the equation becomes y = -.0334 * x + 16.008\r<BR>\n" );
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document.write( "when x = 0, you have a full tank.<BR>\n" );
document.write( "when x = 120, you have -.0334 * 120 + 16.008 = 12<BR>\n" );
document.write( "when x = 220, you have -.0334 * 220 + 16.008 = 8.66\r<BR>\n" );
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document.write( "to find out when the tank will be empty, set y = 0 to get 0 = -.0334 * x + 16.008.<BR>\n" );
document.write( "subtract 16.008 from both sides of this equation to get -16.008 = -.0334 * x.<BR>\n" );
document.write( "divide both sides of this equation by .0334 to get -16.008 / .0334 = x.<BR>\n" );
document.write( "solve for x to get x = -16.008 / .0334 = 479.2814371.\r<BR>\n" );
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document.write( "the tank will be empty after the car has driven 479.2814371 miles.\r<BR>\n" );
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document.write( "the equation can be graphed.<BR>\n" );
document.write( "the graph looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/120903.jpg\" alt=\"$$$\">\r<BR>\n" );
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document.write( "since you tank holds 16.008 gallons of gas and you can travel 499.2814371 miles before you run out of gas, then your gas mileage is equal to 479.2814371 / 16.008 = 29.94011976 miles per gallon.\r<BR>\n" );
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document.write( "that's approximately equal to 30 miles per gallon based on 16 gallon capacity  and 480 miles range.\r<BR>\n" );
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