document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=81763>Question 81763</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine which two equations represent perpendicular lines.<BR>\n" );
document.write( "a)y=5/3x-3<BR>\n" );
document.write( "b)y=3x-5/3<BR>\n" );
document.write( "c)y=-1/3x+5/3<BR>\n" );
document.write( "d)y=1/3x-5/3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58589 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=58589\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For lines to be perpendicular their slopes have to be negative inversions of each other.<BR>\n" );
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document.write( "Examples: <BR>\n" );
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document.write( "If one line has a slope of +8 the other line must have a slope of -1/8 for them to be <BR>\n" );
document.write( "perpendicular.<BR>\n" );
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document.write( "If one line has a slope of -6 the other line must have a slope of +1/6 for them to be <BR>\n" );
document.write( "perpendicular.<BR>\n" );
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document.write( "If one line has a slope of +1/4 the other line must have a slope of -4 for them to be <BR>\n" );
document.write( "perpendicular.<BR>\n" );
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document.write( "If one line has a slope of -1/2 the other line must have a slope of +2 for them to be <BR>\n" );
document.write( "perpendicular.<BR>\n" );
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document.write( "As you can see, the rule is (in non-math terms) given one slope, flip it over and change<BR>\n" );
document.write( "the sign\" and that will give you the slope of the other.<BR>\n" );
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document.write( "Given a slope of 10 (or 10/1) flip it over to get 1/10 and change the sign to minus<BR>\n" );
document.write( "to get the slope of the perpendicular as -1/10.<BR>\n" );
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document.write( "Now to your problem ... all the equations you were given are in the slope intercept <BR>\n" );
document.write( "form ... y = mx + b.  m, the multiplier of x is the slope. So let's look at the slope for<BR>\n" );
document.write( "each equation:<BR>\n" );
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document.write( "a) y=(5/3)x-3<BR>\n" );
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document.write( "The slope in this equation is (5/3). To find the slope of the line that is perpendicular<BR>\n" );
document.write( "to this line, flip the slope to 3/5 and change the sign to minus.  A perpendicular<BR>\n" );
document.write( "line will therefore, have a slope of -3/5.  None of the other equations has that slope.\r<BR>\n" );
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document.write( "b) y=3x-5/3<BR>\n" );
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document.write( "In this equation, the slope of the graph (that is, the multiplier of x is +3. To find the<BR>\n" );
document.write( "slope of a line perpendicular to it, flip it over to 1/3 and change the sign to minus.<BR>\n" );
document.write( "The slope of a perpendicular line will therefore be -1/3.  Notice that equation c) has<BR>\n" );
document.write( "this slope. This tells you that the graph of equation c) is a line that is perpendicular<BR>\n" );
document.write( "to the graph of equation b). But let's work the remaining two equations, just for practice.<BR>\n" );
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document.write( "c) y=-1/3x+5/3<BR>\n" );
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document.write( "The slope of the graph of this equation is (according to its equation) -1/3.  Therefore,<BR>\n" );
document.write( "the graph of a line perpendicular to it will have a slope of (flip and change signs)<BR>\n" );
document.write( "+3/1 or just +3.  The graph of equation b) has that slope ... which we already knew.<BR>\n" );
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document.write( "d) y=1/3x-5/3<BR>\n" );
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document.write( "The graph of this equation has a slope of 1/3, so the graph of a line that is perpendicular<BR>\n" );
document.write( "must have (flip and change signs) a slope of -3/1 or just -3.  None of the other three<BR>\n" );
document.write( "equations has this slope. b) comes close, but the sign of the slope in b) is plus, not<BR>\n" );
document.write( "minus 3 so it is not close to being perpendicular.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to work it.  The answer is again,<BR>\n" );
document.write( "that the graphs of equations b) and c) are the perpendicular pair.<BR>\n" );
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