document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121214>Question 121214</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 6. Are the following pairs of line parallel, perpendicular, or neither.<BR>\n" );
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document.write( "L1 with equation x + 2y = 4<BR>\n" );
document.write( "L2 with equation 2x + 4y =5<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 #88935 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=88935\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First convert the standard equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y=4 ALIGN=MIDDLE  ALT=\"x%2B2y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > into slope intercept form\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=converting_linear_equations.solver>Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%2B2y=4 ALIGN=MIDDLE  ALT=\"1x%2B2y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%2B2y-1x=4-1x ALIGN=MIDDLE  ALT=\"1x%2B2y-1x=4-1x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1x from both sides<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=-1x%2B4 ALIGN=MIDDLE  ALT=\"2y=-1x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282y%29%2F%282%29=%28-1x%2B4%29%2F%282%29 ALIGN=MIDDLE  ALT=\"%282y%29%2F%282%29=%28-1x%2B4%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2 to isolate y<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1x%29%2F%282%29%2B%284%29%2F%282%29 ALIGN=MIDDLE  ALT=\"y+=+%28-1x%29%2F%282%29%2B%284%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction on the right hand side<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F2%29x%2B2 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F2%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce and simplify<br><br><br>The original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%2B2y=4 ALIGN=MIDDLE  ALT=\"1x%2B2y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (standard form) is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F2%29x%2B2 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F2%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (slope-intercept form)<br><br><br>The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F2%29x%2B2 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F2%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the 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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F2 ALIGN=MIDDLE  ALT=\"m=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the y intercept.<br><br><br></TD></TR>\n" );
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document.write( "Now convert the standard equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B4y=5 ALIGN=MIDDLE  ALT=\"2x%2B4y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > into slope intercept form\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=converting_linear_equations.solver>Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B4y=5 ALIGN=MIDDLE  ALT=\"2x%2B4y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B4y-2x=5-2x ALIGN=MIDDLE  ALT=\"2x%2B4y-2x=5-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2x from both sides<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=-2x%2B5 ALIGN=MIDDLE  ALT=\"4y=-2x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284y%29%2F%284%29=%28-2x%2B5%29%2F%284%29 ALIGN=MIDDLE  ALT=\"%284y%29%2F%284%29=%28-2x%2B5%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4 to isolate y<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2x%29%2F%284%29%2B%285%29%2F%284%29 ALIGN=MIDDLE  ALT=\"y+=+%28-2x%29%2F%284%29%2B%285%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction on the right hand side<br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F2%29x%2B5%2F4 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F2%29x%2B5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce and simplify<br><br><br>The original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B4y=5 ALIGN=MIDDLE  ALT=\"2x%2B4y=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (standard form) is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F2%29x%2B5%2F4 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F2%29x%2B5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (slope-intercept form)<br><br><br>The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F2%29x%2B5%2F4 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F2%29x%2B5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the 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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F2 ALIGN=MIDDLE  ALT=\"m=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slope and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5%2F4 ALIGN=MIDDLE  ALT=\"b=5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the y intercept.<br><br><br></TD></TR>\n" );
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document.write( "Since the two slopes are both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F2 ALIGN=MIDDLE  ALT=\"m=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the two slopes are equal. This also means that the two lines are parallel\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the lines <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+2y+=+4 ALIGN=MIDDLE  ALT=\"x+%2B+2y+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+4y+=5 ALIGN=MIDDLE  ALT=\"2x+%2B+4y+=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > are parallel. </SPAN>\n" );
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