document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190802>Question 190802</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here's another problem I could use some help on. I would really be greatful to anyone who can help me. Thanks                                                                          The line y=0.15x+0.79                                                                    represents an estimate of the average cost of gasoline for each year.                                                                           The line 0.11x-y=-0.85<BR>\n" );
document.write( "estimates the price of gasoline in January of each year (Bureau of Labor Statistics, 2006). <BR>\n" );
document.write( "a)Do you expect the lines to be intersecting, parallel, or perpendicular? <BR>\n" );
document.write( "b)Work the equations of the lines to determine if they are parallel. <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 #143407 by </B><A HREF=/tutors/aboutme.mpl?userid=jojo14344><B>jojo14344(1513)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jojo14344><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=143407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Tahoma\" size=1.5><BR>\n" );
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document.write( "The line <font color=blue>y=0.15x+0.79</font> (EQN 1) represents an estimate of the average cost of gasoline for each year. The line <font color=blue>0.11x-y=-0.85</font> (EQN 2 ) estimates the price of gasoline in January of each year (Bureau of Labor Statistics, 2006). \r<BR>\n" );
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document.write( "* Just by looking on the Line Eqns., the 2 lines are neither parallel nor perpendicular - because of the Slope. <BR>\n" );
document.write( "If they intersect, we'll see:\r<BR>\n" );
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document.write( "EQN 1, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.15x%2B0.79 ALIGN=MIDDLE  ALT=\"y=0.15x%2B0.79\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "Let fy=0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0.15x%2B0.79 ALIGN=MIDDLE  ALT=\"0=0.15x%2B0.79\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.15x=-0.79 ALIGN=MIDDLE  ALT=\"0.15x=-0.79\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%280.15%29x%2Fcross%280.15%29=cross%28-0.79%295.27%2Fcross%280.15%29 ALIGN=MIDDLE  ALT=\"cross%280.15%29x%2Fcross%280.15%29=cross%28-0.79%295.27%2Fcross%280.15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28x=-5.27%29 ALIGN=MIDDLE  ALT=\"red%28x=-5.27%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > X-Intercept\r<BR>\n" );
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document.write( "Let fx=o:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.15%280%29%2B0.79 ALIGN=MIDDLE  ALT=\"y=0.15%280%29%2B0.79\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28y=0.79%29 ALIGN=MIDDLE  ALT=\"red%28y=0.79%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Y-Intercept\r<BR>\n" );
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document.write( "EQN 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.11x-y=-0.85 ALIGN=MIDDLE  ALT=\"0.11x-y=-0.85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let fy=0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.11%28x%29-0=-0.85 ALIGN=MIDDLE  ALT=\"0.11%28x%29-0=-0.85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%280.11%29x%2Fcross%280.11%29=cross%28-0.85%297.73%2Fcross%280.11%29 ALIGN=MIDDLE  ALT=\"cross%280.11%29x%2Fcross%280.11%29=cross%28-0.85%297.73%2Fcross%280.11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28x=-7.73%29 ALIGN=MIDDLE  ALT=\"red%28x=-7.73%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, X-Interecpt\r<BR>\n" );
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document.write( "Let fx=0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.11%280%29-y=-0.85 ALIGN=MIDDLE  ALT=\"0.11%280%29-y=-0.85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28y=0.85%29 ALIGN=MIDDLE  ALT=\"red%28y=0.85%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Y-Intercept\r<BR>\n" );
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document.write( "We'll see the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-10%2C8%2C-2%2C2%2Cgraph%28500%2C500%2C-10%2C8%2C-2%2C2%2C0.15x%2B0.79%2C0.11x%2B0.85%29%2Cblue%28circle%28-5.27%2C0%2C.12%29%29%2Cblue%28circle%280%2C0.79%2C0.12%29%29%2Cblue%28circle%28-7.73%2C0%2C.12%29%29%2Cblue%28circle%280%2C0.85%2C.12%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28RED=EQN1%29 ALIGN=MIDDLE  ALT=\"red%28RED=EQN1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28GREEN=EQN2%29 ALIGN=MIDDLE  ALT=\"green%28GREEN=EQN2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, as we see the 2 lines intersect, and we calculate the exact point.\r<BR>\n" );
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document.write( "Substitute EQN 1 to EQN 2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.11x-highlight%280.15x%2B0.79+%29=-0.85 ALIGN=MIDDLE  ALT=\"0.11x-highlight%280.15x%2B0.79+%29=-0.85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.11x-0.15x-0.79=-0.85 ALIGN=MIDDLE  ALT=\"0.11x-0.15x-0.79=-0.85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.04x=-0.85%2B0.79=-0.06 ALIGN=MIDDLE  ALT=\"-0.04x=-0.85%2B0.79=-0.06\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28-0.04%29x%2Fcross%28-0.04%29=cross%28-0.06%291.5%2Fcross%28-0.04%29 ALIGN=MIDDLE  ALT=\"cross%28-0.04%29x%2Fcross%28-0.04%29=cross%28-0.06%291.5%2Fcross%28-0.04%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28x=1.5%29 ALIGN=MIDDLE  ALT=\"red%28x=1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.5 ALIGN=MIDDLE  ALT=\"x=1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to EQN 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.15%281.5%29%2B0.79=0.225%2B0.79 ALIGN=MIDDLE  ALT=\"y=0.15%281.5%29%2B0.79=0.225%2B0.79\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28y=1.015%29 ALIGN=MIDDLE  ALT=\"red%28y=1.015%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "*The two lines intersect at point <font color=blue>(1.5,1.015)</font>\r<BR>\n" );
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document.write( "Thank you,<BR>\n" );
document.write( "Jojo</font> </SPAN>\n" );
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