document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=157193>Question 157193</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I dont understand what im supposed to do for this problem:<BR>\n" );
document.write( "without graphing, determine if the graphs of each pair of equations are parallel, perpendicular or neither.\r<BR>\n" );
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document.write( "2y=8x+4 and y=-1/4x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #115871 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=115871\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can do this without graphing by finding the slope of each equation.<BR>\n" );
document.write( "Remember the \"slope-intercept\" form? y = mx+b where m is the slope.<BR>\n" );
document.write( "Starting with the given equations, get them into the slope-intercept form so that you campare their slopes:<BR>\n" );
document.write( "First equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+=+8x%2B4 ALIGN=MIDDLE  ALT=\"2y+=+8x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > To get y by itself, you divide both sides by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4x%2B2 ALIGN=MIDDLE  ALT=\"y+=+4x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you can see that the slope, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+4 ALIGN=MIDDLE  ALT=\"m+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Second equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F4%29x ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F4%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > as you can see, this is already in the slope-intercept form and the slope here is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-1%2F4%29 ALIGN=MIDDLE  ALT=\"m+=+%28-1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Ok, we have the two slopes...now what?<BR>\n" );
document.write( "Well, we compare them!<BR>\n" );
document.write( "Why, because we know (or should know) that if two lines are parallel, their slopes are equal, and if two lines are perpendicular, their slopes are negative reciprocals.<BR>\n" );
document.write( "So what is the negative reciprocal of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >?  Why, it's just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F4%29 ALIGN=MIDDLE  ALT=\"%28-1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So you can see that the slopes are negative reciprocals, therefore, the two lines are perpendicular!...and all this without graphing.<BR>\n" );
document.write( " </SPAN>\n" );
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