document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936874>Question 936874</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I would really appreciate your help in the following question.<BR>\n" );
document.write( "Lora has a gift card where all downloads for music cost the same amount. after downloading 2 songs, the balance on her card was $18.10. after downloading a total of 5 songs, the balance was $15.25<BR>\n" );
document.write( "1. write an equation in slope-intercept form that represents the amount in dollars remaining on the card as a function of songs downloaded.<BR>\n" );
document.write( "2. identify the slope of the line and tell what the slope represents.<BR>\n" );
document.write( "3.identify the y intercept of the line and tell what it represents.<BR>\n" );
document.write( "4. how many additional songs can Lora download when there is $15.25 left on the card? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #570325 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=570325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = number of songs that are downloaded.\r<BR>\n" );
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document.write( "when x = 2, the remaining balance is 18.10\r<BR>\n" );
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document.write( "when x = 5, the remaining balance is 15.25\r<BR>\n" );
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document.write( "the slope intercept form of the equation for a straight line is y = mx + b\r<BR>\n" );
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document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept.\r<BR>\n" );
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document.write( "the formula for the slope is:\r<BR>\n" );
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document.write( "m = (y2 - y1) / (x2 - x1)\r<BR>\n" );
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document.write( "(x1,y1) = (2,18.10)<BR>\n" );
document.write( "(x2,y2) = (5,15.25)\r<BR>\n" );
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document.write( "the x-value of the coordinate pair is the number of songs that were downloaded.<BR>\n" );
document.write( "the y-value of the coordinate pair is the remaining balance.\r<BR>\n" );
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document.write( "slope = m = (y2-y1) / (x2-x1) = (15.25 - 18.10) / (5 - 2) = -2.85 / 3 = -.95\r<BR>\n" );
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document.write( "replace m with -.95 in the slope intercept form of the equation to get:\r<BR>\n" );
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document.write( "y = -.95 * x + b\r<BR>\n" );
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document.write( "now you want to solve for b, which is the y-intercept.\r<BR>\n" );
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document.write( "take any one of the point pairs on the line and replace y with the y-coordinate and replace x with the x-coordinate and solve for b.\r<BR>\n" );
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document.write( "we'll use the point (2,18.1)\r<BR>\n" );
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document.write( "y = -.95 * x + b becomes:\r<BR>\n" );
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document.write( "18.1 = -.95 * 2 + b\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "18.1 = -1.9 + b\r<BR>\n" );
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document.write( "add 1.9 to both sides of the equation to get:\r<BR>\n" );
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document.write( "18.1 + 1.9 = -1.9 + 1.9 + b\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "20 = b\r<BR>\n" );
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document.write( "that's your y-intercept.\r<BR>\n" );
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document.write( "the slope intercept form of the equation becomes:\r<BR>\n" );
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document.write( "y = -.95 * x + 20\r<BR>\n" );
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document.write( "answer to question 1:\r<BR>\n" );
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document.write( "the equation is y = -.95 * x + 20\r<BR>\n" );
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document.write( "answer to question 2:\r<BR>\n" );
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document.write( "the y-intercept is 20.\r<BR>\n" );
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document.write( "it represents the remaining balance of the account before any songs were downloaded.\r<BR>\n" );
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document.write( "answer to question 3:\r<BR>\n" );
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document.write( "find out the x-intercept.\r<BR>\n" );
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document.write( "the x-intercept is the value of x when y is equal to 0.\r<BR>\n" );
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document.write( "this will be when there is no more money remaining in the account.\r<BR>\n" );
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document.write( "find this by setting y = 0 and solving for x.\r<BR>\n" );
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document.write( "equation of y = -.95 * x + 20 becomes:\r<BR>\n" );
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document.write( "0 = -.95 * x + 20\r<BR>\n" );
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document.write( "subtract 20 from both sides of this equation to get:\r<BR>\n" );
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document.write( "-20 = -.95 * x + 20 - 20\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "-20 = -.95 * x\r<BR>\n" );
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document.write( "divide both sides of this equation by -.95 to get:\r<BR>\n" );
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document.write( "-20 / -.95 = x\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 21.0505263158 which we can rounded off to 21.05.\r<BR>\n" );
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document.write( "when she bought 21 cd, she had a small balance left.\r<BR>\n" );
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document.write( "that balance is y = -.95 * 21 + 20 = .05 dollars which is equal to 5 cents.\r<BR>\n" );
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document.write( "there's not enough money left in the account to buy another song, so this is her limit.\r<BR>\n" );
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document.write( "when she had 15.25 remaining balance, she had already bought 5 songs.\r<BR>\n" );
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document.write( "she will run out of money when she buys 21 songs.\r<BR>\n" );
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document.write( "she can buy an additional 21 - 5 = 16 songs before she runs out of money.\r<BR>\n" );
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document.write( "this can all be represented on the graph, which is shown below:\r<BR>\n" );
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document.write( " </SPAN>\n" );
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