document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132638>Question 1132638</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The line y= -12/5 x + 2 is exactly 3 units away from two other lines parallel to it.The distance in units between the y-intercepts of these two other lines is. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749830 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=749830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The slope of the line is -12/5, and the slope of the line perpendicular to that is 5/12.\r<BR>\n" );
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document.write( "this is the general form of the line perpendicular to the given line.<BR>\n" );
document.write( "We want to go 3 units out on the perpendicular.  <BR>\n" );
document.write( "Suppose the perpendicular is to the line at the x-intercept of (5/6, 0). Then the line can be shown using the point slope formula of y-y1=m(x-x1), where m is slope and (x1, y1) are (5/6, 0) to be y=(5/12)x-(25/72)<BR>\n" );
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document.write( "Going to the right 3 units is a right triangle with the line 3 units away.  The length of the hypotenuse is where the x-intercept is for that line.  The angle for a slope of 5/12 is where the tangent of an angle is 5/12, which is arc tan (5/12) or 22.62 degrees.\r<BR>\n" );
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document.write( "So cos 22.62 =3/hypot<BR>\n" );
document.write( "hypot=3/cos 22.62=3.25 units away from (5/6, 0) so the x-intercept of that line is 3.25+5/6 or (4.08, 0)<BR>\n" );
document.write( "We know the slope of this parallel line is -2.4, and we have a point, so the equation of the line is y=-2.4(x-4.08)=y=-2.4x+9.08.  \r<BR>\n" );
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document.write( "The distance to the x-intercept in the other direction is -3.25 units, so the x-intercept is at -3.25+5/6=-2.42 or (-2.42, 0)\r<BR>\n" );
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document.write( "The equation of this line is y=-2.4(x+2.42)=-2.4x-5.8\r<BR>\n" );
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document.write( "The distance between the two y-intercepts is 9.08-(-5.8)=14.88 units ANSWER\r<BR>\n" );
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document.write( " </SPAN>\n" );
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