document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1035086>Question 1035086</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Distance between the lines 5x+12y-1=0 and 10x+24y+k=0 is 2 then the value of k is </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649706 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=649706\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Change this description a little bit.  The slopes of both lines must be  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F12 ALIGN=MIDDLE  ALT=\"5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the description to be meaningful.  The two equations of these lines are then  5x+12y-1=0  and  5x+12y+j=0,  and you want to find j.  The two lines are parallel, and the distance between them is 2.\r<BR>\n" );
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document.write( "Here is 5x+12y-1=0 graphed:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-3%2C4%2C-3%2C4%2C-5x%2F12%2B1%2F12%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-3%2C4%2C-3%2C4%2C-5x%2F12%2B1%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The equation can also be stated <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%285%2F12%29x%2B1%2F12 ALIGN=MIDDLE  ALT=\"y=-%285%2F12%29x%2B1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Choose a convenient point on this line, maybe  the x-intercept,  ( 1/5 ,0).\r<BR>\n" );
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document.write( "You want the other line,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B12y%2Bj=0 ALIGN=MIDDLE  ALT=\"5x%2B12y%2Bj=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to be 2 unit away from  5x+12y-1=0; and you can pick either above OR below.  Put the equation of the line you wish to find in slope-intercept form, as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%285%2F12%29x-j%2F12 ALIGN=MIDDLE  ALT=\"y=-%285%2F12%29x-j%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Summarizing all this,  we want  distance from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%285%2F12%29x%2B1%2F12 ALIGN=MIDDLE  ALT=\"y=-%285%2F12%29x%2B1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%285%2F12%29x-j%2F12 ALIGN=MIDDLE  ALT=\"y=-%285%2F12%29x-j%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  to be equal to 2.  To be much more specific, referring to a given or desired point on the first line graphed,  <b>we want  the distance between  ( 1/5, 0 ) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%285%2F12%29x%2Bj%2F12 ALIGN=MIDDLE  ALT=\"y=-%285%2F12%29x%2Bj%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  to be equal to 2.</b>\r<BR>\n" );
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document.write( "Keep reading and thinking on that.<BR>\n" );
document.write( "A general point for the equation of the line you want to find is an ordered pair point   ( x, -(5/12)x+j/12 ).<BR>\n" );
document.write( "When you have this then use the distance formula to set up the equation necessary to solve for j. </SPAN>\n" );
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