document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970369>Question 970369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which best describes the relationship between the lines with the equations 9x-2y=5 and -9x+9y=9?<BR>\n" );
document.write( "[A] parallel<BR>\n" );
document.write( "[B] perpendicular <BR>\n" );
document.write( "[C] neither parallel nor perpendicular <BR>\n" );
document.write( "[D] same line    </SPAN>\n" );
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document.write( "Which best describes the relationship between the lines with the equations <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9x-2y=5 ALIGN=MIDDLE  ALT=\"+9x-2y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9x%2B9y=9 ALIGN=MIDDLE  ALT=\"-9x%2B9y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "[A] parallel <BR>\n" );
document.write( "[B] perpendicular <BR>\n" );
document.write( "[C] neither parallel nor perpendicular <BR>\n" );
document.write( "[D] same line \r<BR>\n" );
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document.write( "to find out, we need a slope;as you know, two lines  <BR>\n" );
document.write( "that have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=same ALIGN=MIDDLE  ALT=\"same\"   DISABLED_style= \"max-width:90%; height:auto;\" > slope are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallel ALIGN=MIDDLE  ALT=\"parallel\"   DISABLED_style= \"max-width:90%; height:auto;\" >,and do not intercept, there is no solution   <BR>\n" );
document.write( "two lines  that have  slope negative reciprocal to each other are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=perpendicular ALIGN=MIDDLE  ALT=\"perpendicular\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where the lines lie on top of each other, one equation can be rearranged to be the other equation precisely; this means when solving, you would get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=y ALIGN=MIDDLE  ALT=\"y=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=x ALIGN=MIDDLE  ALT=\"x=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there are infinite solutions in this case (every point along the line would be a solution)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9x-2y=5 ALIGN=MIDDLE  ALT=\"+9x-2y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9x%2B9y=9 ALIGN=MIDDLE  ALT=\"-9x%2B9y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >?<BR>\n" );
document.write( "so, first write both equations in a slope-intercept form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x-2y=5 ALIGN=MIDDLE  ALT=\"9x-2y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x-5=2y ALIGN=MIDDLE  ALT=\"9x-5=2y\"   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=%289%2F2%29x-5%2F5 ALIGN=MIDDLE  ALT=\"y=%289%2F2%29x-5%2F5\"   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=%289%2F2%29x-1 ALIGN=MIDDLE  ALT=\"y=%289%2F2%29x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> a slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F2%29 ALIGN=MIDDLE  ALT=\"%289%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and y-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9x%2B9y=9 ALIGN=MIDDLE  ALT=\"-9x%2B9y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >....both sides divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   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=-x%2By=1 ALIGN=MIDDLE  ALT=\"-x%2By=1\"   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=x%2B1 ALIGN=MIDDLE  ALT=\"y=x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> a slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and y-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, both the lines have different slopes and different y- intercept which means the lines  neither parallel nor perpendicular \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2Cx%2B1%2C+%289%2F2%29x-1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2Cx%2B1%2C+%289%2F2%29x-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "that all  leads us  to the conclusion that your answer is: [C] </SPAN>\n" );
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