document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=183218>Question 183218</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This problem has more than one part, please HELP ME put it all together.?<BR>\n" );
document.write( "The price of unleaded regular gasoline varies with the price per barrel of oil on the world market. When oil was selling for $30 per barrel I paid $1.25 per gallon for gasoline. When oil was selling for $140 per barrel, I paid $4.00 for a gallon of gasoline. I have to make a table showing the above data for gasoline and oil prices. Then, I have to construct a graph with oil price per barrel on the horizontal axis and the price per gallon of gasoline on the vertical axis, then plot the two points given and draw a line connecting the two points and extending over the range of $0 to $150 for the price of a barrel of oil, and find the slope of the line, then find the “y” intercept for the line (the point where oil is $0.00 per barrel) and finally write the equation of the line. Assuming that the relationship is linear, I have to calculate the price for a gallon of gasoline when the oil price reaches $39.34 per barrel. How does this compare to the price you are paying today?\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 #137565 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=137565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=price per barrel of oil and y=price per gallon of gasoline\r<BR>\n" );
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document.write( "First translation: \"When oil was selling for $30 per barrel I paid $1.25 per gallon for gasoline\" means that when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=130 ALIGN=MIDDLE  ALT=\"x=130\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1.25 ALIGN=MIDDLE  ALT=\"y=1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So we have one point (130,1.25)\r<BR>\n" );
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document.write( "Second translation: \"When oil was selling for $140 per barrel, I paid $4.00 for a gallon of gasoline\" means that when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=140 ALIGN=MIDDLE  ALT=\"x=140\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So we have another point (140,4)\r<BR>\n" );
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document.write( "So here's the table of the two ordered pairs (points)<BR>\n" );
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document.write( "<th>x</th><th>y</th>\r\n" );
document.write( "<tr><TD >130</TD><TD >1.25</TD></tr>\r\n" );
document.write( "<tr><TD >140</TD><TD >4</TD></tr>\r\n" );
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document.write( "Now set up the axis (with the proper ranges and labels)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/step1-1.png\">\r<BR>\n" );
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document.write( "Plot the two points\r<BR>\n" );
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document.write( "Draw a line through the points (in blue)\r<BR>\n" );
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document.write( "Now let's find the equation of the line that goes through the points (130,1.25) and (140,4)\r<BR>\n" );
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document.write( "First let's find the slope of the line through the points (130,1.25) and (140,4)\r<BR>\n" );
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document.write( "Note: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(x_{1}, y_{1}\right)\"> is the first point (130,1.25) and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(x_{2}, y_{2}\right)\"> is the second point (140,4)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the slope formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%284-1.25%29%2F%28140-130%29 ALIGN=MIDDLE  ALT=\"m=%284-1.25%29%2F%28140-130%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D=4 ALIGN=MIDDLE  ALT=\"y%5B2%5D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=1.25 ALIGN=MIDDLE  ALT=\"y%5B1%5D=1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=140 ALIGN=MIDDLE  ALT=\"x%5B2%5D=140\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=130 ALIGN=MIDDLE  ALT=\"x%5B1%5D=130\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%282.75%29%2F%28140-130%29 ALIGN=MIDDLE  ALT=\"m=%282.75%29%2F%28140-130%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.25 ALIGN=MIDDLE  ALT=\"1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.75 ALIGN=MIDDLE  ALT=\"2.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%282.75%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"m=%282.75%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=130 ALIGN=MIDDLE  ALT=\"130\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140 ALIGN=MIDDLE  ALT=\"140\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0.275 ALIGN=MIDDLE  ALT=\"m=0.275\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So the slope of the line that goes through the points (130,1.25) and (140,4) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0.275 ALIGN=MIDDLE  ALT=\"m=0.275\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now let's use the point slope formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the point slope formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1.25=0.275%28x-130%29 ALIGN=MIDDLE  ALT=\"y-1.25=0.275%28x-130%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0.275 ALIGN=MIDDLE  ALT=\"m=0.275\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=130 ALIGN=MIDDLE  ALT=\"x%5B1%5D=130\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=1.25 ALIGN=MIDDLE  ALT=\"y%5B1%5D=1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1.25=0.275x%2B0.275%28-130%29 ALIGN=MIDDLE  ALT=\"y-1.25=0.275x%2B0.275%28-130%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1.25=0.275x-35.75 ALIGN=MIDDLE  ALT=\"y-1.25=0.275x-35.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.275x-35.75%2B1.25 ALIGN=MIDDLE  ALT=\"y=0.275x-35.75%2B1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.25 ALIGN=MIDDLE  ALT=\"1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.275x-34.5 ALIGN=MIDDLE  ALT=\"y=0.275x-34.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So the equation that goes through the points (130,1.25) and (140,4) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.275x-34.5 ALIGN=MIDDLE  ALT=\"y=0.275x-34.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The equation is now in slope intercept form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0.275 ALIGN=MIDDLE  ALT=\"m=0.275\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the y-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-34.5 ALIGN=MIDDLE  ALT=\"b=-34.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note:\r<BR>\n" );
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document.write( "Since the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0.275 ALIGN=MIDDLE  ALT=\"m=0.275\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that for every dollar increase that the price per barrel of oil experiences, the price per gallon of gas will increase $0.275\r<BR>\n" );
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document.write( "Also, the y-intercept is the value when the price of oil is $0 per barrel. So if the price per barrel is $0, then the price of gas is -34.50 dollars. \r<BR>\n" );
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document.write( "\"Assuming that the relationship is linear, I have to calculate the price for a gallon of gasoline when the oil price reaches $39.34 per barrel\"\r<BR>\n" );
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document.write( "In this case, we want to know \"y\" when \"x\" is equal to 39.34. So simply plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=39.34 ALIGN=MIDDLE  ALT=\"x=39.34\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find \"y\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.275x-34.5 ALIGN=MIDDLE  ALT=\"y=0.275x-34.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the equation we just found\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.275%2839.34%29-34.5 ALIGN=MIDDLE  ALT=\"y=0.275%2839.34%29-34.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=39.34 ALIGN=MIDDLE  ALT=\"x=39.34\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10.8185-34.5 ALIGN=MIDDLE  ALT=\"y=10.8185-34.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-23.6815 ALIGN=MIDDLE  ALT=\"y=-23.6815\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract\r<BR>\n" );
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document.write( "So when the price of oil is $39.34 a barrel, the price of gas will be about -23.68 dollars a barrel.\r<BR>\n" );
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document.write( "Note: the relationship between the price of oil and the price of gas is a little more complex than just a simple linear relationship (since there are more factors involved).  </SPAN>\n" );
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