document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208435>Question 208435</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Parallel and Perpendicular Slope\r<BR>\n" );
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document.write( "Please help me solve this equation: Which lines are parallel?<BR>\n" );
document.write( "a.x=7<BR>\n" );
document.write( "b.y=5/6x+8<BR>\n" );
document.write( "c.y=5/6x-4<BR>\n" );
document.write( "d.x=9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157658 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=157658\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -----<BR>\n" );
document.write( "if the slopes are the same, then the lines are parallel.<BR>\n" );
document.write( "if the slopes are negative reciprocals of each other than the lines are perpendicular.<BR>\n" );
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document.write( "your choices are:<BR>\n" );
document.write( "a.x=7<BR>\n" );
document.write( "b.y=5/6x+8<BR>\n" );
document.write( "c.y=5/6x-4<BR>\n" );
document.write( "d.x=9<BR>\n" );
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document.write( "b and c are parallel to each other because they have the same slope.<BR>\n" );
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document.write( "a and d are parallel to each other because they are both perpendicular to the x axis at that point and are therefore parallel to each other.<BR>\n" );
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document.write( "first b and c.<BR>\n" );
document.write( "graph is of y = 5/6x + 8 and y = 5/6x -4<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%285%2F6%29x+%2B+8%2C+%285%2F6%29x+-+4%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%285%2F6%29x+%2B+8%2C+%285%2F6%29x+-+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "next a and c.<BR>\n" );
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document.write( "i can't draw them directly on algebra.com but i can fudge the normal equation to make them look vertical, or almost vertical.<BR>\n" );
document.write( "doing that, they will look like this.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-1%2C10%2C-10%2C10%2C1000000%2F%28x-7%29%2C1000000%2F%28x-9%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1%2C10%2C-10%2C10%2C1000000%2F%28x-7%29%2C1000000%2F%28x-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "you can see that both lines are perpendicular to the x-axis and therefore parallel to each other.<BR>\n" );
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document.write( "having the same slope was easy to show mathematically with b and c.<BR>\n" );
document.write( "showing that a and d have the same slope is a lot harder.<BR>\n" );
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document.write( "trust me, they are.<BR>\n" );
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document.write( "the problem stems from the fact that their slope is equal to infinity which is not a real number because it's undefined.<BR>\n" );
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document.write( "nevertheless, both their slopes are equal to infinity so i would say they are equal to each other even though there are people who would argue otherwise.  can one infinity really be larger than another?<BR>\n" );
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document.write( "since both these lines are perpendicular to the x-axis, which is a fact not in dispute as far as i known, then both their slopes are negative reciprocals of 0 which should also strengthen the argument that their slopes are equal.<BR>\n" );
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document.write( "bottom line is they threw you a wrinkle when they gave you the equations of x = 7 and x = 9.<BR>\n" );
document.write( "these lines are clearly parallel to each other but proving it leads into the murky world of infinity which has stumped smarter persons than me.<BR>\n" );
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