document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112978>Question 112978</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0078660130/algebrahomeworkh>Geometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Hi can you please show me how to find the distance between the parallel lines<BR>\n" );
document.write( ":y=2x-4 and y=2x+1<BR>\n" );
document.write( "Thank you <BR>\n" );
document.write( "Nicole<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 #82304 by </B><A HREF=/tutors/aboutme.mpl?userid=veronica0626><B>veronica0626(5)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=veronica0626><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=82304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-6%2C+5%2C+-10%2C+10%2C+2x-4%2C+2x%2B1%2C+-2x%2B1+%29 ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-6%2C+5%2C+-10%2C+10%2C+2x-4%2C+2x%2B1%2C+-2x%2B1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First we need to know that the distance between parallel line is the distance of EVERY segment perpendicular to the given lines.\r<BR>\n" );
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document.write( "we emphasize the word every because the distance is equal for every segment.\r<BR>\n" );
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document.write( "to find that segment we should name one line perpendicular to the two given lines.<BR>\n" );
document.write( "(any line perpindicular would do)\r<BR>\n" );
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document.write( "since the slope of the parallel lines is 2, the slope of the line perpendicular to it is -2 (there's a theorem for that)\r<BR>\n" );
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document.write( "i name my perpendicular line y=-2x+1 represented by the blue line<BR>\n" );
document.write( "(y=2x+4 is red and y=2x+1 is green)\r<BR>\n" );
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document.write( "then we find the intersection of y=2x+1 and y=-2x+1\r<BR>\n" );
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document.write( "by elimination or substitution<BR>\n" );
document.write( "we get x=0 and y=1/2, then the intersection is (0,1/2)\r<BR>\n" );
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document.write( "and the intersection of y=2x-4 and y=-2x+1<BR>\n" );
document.write( "by elimination or substition<BR>\n" );
document.write( "we get x=3/4 and y 5/2, then the intersection is (3/4 , 5/2)\r<BR>\n" );
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document.write( "these points are the endpoints of the segment perpendicular to the given lines.\r<BR>\n" );
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document.write( "getting the distance, we follow the formula<BR>\n" );
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