document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=987825>Question 987825</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me understand how to determine if these pairs of lines are perpendicular parallel or neither:\r<BR>\n" );
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document.write( "1. y = 4/3<BR>\n" );
document.write( "2. -4x = 3<BR>\n" );
document.write( "3. x = 4/3   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #608540 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=608540\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, put all equations in the \"slope-intercept\" 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;\" >\r<BR>\n" );
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document.write( "If two lines are perpendicular, their slopes are the negative reciprocal of each other.<BR>\n" );
document.write( "If two lines are parallel, their slopes are same.<BR>\n" );
document.write( "If the slope values are not the same, so the lines are not parallel. <BR>\n" );
document.write( "If the slope values are not negative reciprocals either, so the lines are not perpendicular. Then the answer is \"neither\".\r<BR>\n" );
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document.write( "you are given:\r<BR>\n" );
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document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4%2F3 ALIGN=MIDDLE  ALT=\"y+=+4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.1<BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x+=+3 ALIGN=MIDDLE  ALT=\"-4x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.2<BR>\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4%2F3 ALIGN=MIDDLE  ALT=\"x+=+4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >......eq.3\r<BR>\n" );
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document.write( "put all equations in the \"slope-intercept\" form\r<BR>\n" );
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document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0%2Ax%2B4%2F3 ALIGN=MIDDLE  ALT=\"y+=+0%2Ax%2B4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.1=> slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0 ALIGN=MIDDLE  ALT=\"m=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, y-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4%2F3 ALIGN=MIDDLE  ALT=\"b=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >; so, this line is a horizontal line that intercept y-axis at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x+=+3 ALIGN=MIDDLE  ALT=\"-4x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.2 => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=4x%2B3 ALIGN=MIDDLE  ALT=\"0=4x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=-3 ALIGN=MIDDLE  ALT=\"4x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F4 ALIGN=MIDDLE  ALT=\"x=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the line is vertical and slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+undefined ALIGN=MIDDLE  ALT=\"+undefined\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F4 ALIGN=MIDDLE  ALT=\"x=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >; \r<BR>\n" );
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document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4%2F3 ALIGN=MIDDLE  ALT=\"x+=+4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >......eq.3=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2F3 ALIGN=MIDDLE  ALT=\"x=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the line is vertical and slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+undefined ALIGN=MIDDLE  ALT=\"+undefined\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x-intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2F3 ALIGN=MIDDLE  ALT=\"x=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, line 1 (which is horizontal line) and 2 (which is vertical line) 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;\" > to each other\r<BR>\n" );
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document.write( "so, line 1 (which is horizontal line) and 3 (which is vertical line) 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;\" > to each other\r<BR>\n" );
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document.write( "so, line 2 (which is vertical line) and 3 (which is vertical line) 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;\" > to each other\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Aline%284%2F3%2C10%2C4%2F3%2C-10%29%2C%0D%0Aline%28-3%2F4%2C10%2C-3%2F4%2C-10%29%2C%0D%0Agraph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4%2F3%2C4%2F3%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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