document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=359558>Question 359558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> From the distance from (-4,-1) to the line defined by y=-2x+1. Express as a radical or a number rounded to the nearest hundredth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #256552 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=256552\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B1 ALIGN=MIDDLE  ALT=\"y=-2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The closest distance is formed by the line perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B1 ALIGN=MIDDLE  ALT=\"y=-2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > that goes through the point (-4,-1).<BR>\n" );
document.write( "To find the perpendicular line, use the slope since perpendicular lines have slopes that are negative reciprocals.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D%2Am%5B2%5D=-1 ALIGN=MIDDLE  ALT=\"m%5B1%5D%2Am%5B2%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Am%5B2%5D=-1 ALIGN=MIDDLE  ALT=\"-2%2Am%5B2%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D=1%2F2 ALIGN=MIDDLE  ALT=\"m%5B2%5D=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now use the point slope form of a line, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5Bp%5D=m%28x-x%5Bp%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5Bp%5D=m%28x-x%5Bp%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%28-1%29=%281%2F2%29%28x-%28-4%29%29 ALIGN=MIDDLE  ALT=\"y-%28-1%29=%281%2F2%29%28x-%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B1=%281%2F2%29%28x%2B4%29 ALIGN=MIDDLE  ALT=\"y%2B1=%281%2F2%29%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B2=x%2B4 ALIGN=MIDDLE  ALT=\"2y%2B2=x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B2y=2 ALIGN=MIDDLE  ALT=\"-x%2B2y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now that you have both lines, find the intersection of the two lines. <BR>\n" );
document.write( "The distance you're after is the distance from point (-4,-1) to the intersection point.<BR>\n" );
document.write( "Substitute eq. 1 into eq. 2 and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B2%28-2x%2B1%29=2 ALIGN=MIDDLE  ALT=\"-x%2B2%28-2x%2B1%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x-4x%2B2=2 ALIGN=MIDDLE  ALT=\"-x-4x%2B2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x=0 ALIGN=MIDDLE  ALT=\"-5x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then from eq. 1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%280%29%2B1 ALIGN=MIDDLE  ALT=\"y=-2%280%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-5%2C5%2Cgrid%281%29%2Ccircle%28-4%2C-1%2C0.2%29%2Ccircle%280%2C1%2C0.2%29%2Cgraph%28300%2C300%2C-5%2C5%2C-5%2C5%2C-2x%2B1%2C%282%2Bx%29%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now use the distance formula to find the distance from (-4,-1) to (0,1).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2 ALIGN=MIDDLE  ALT=\"D%5E2=%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=%280-%28-4%29%29%5E2%2B%281-%28-1%29%29%5E2 ALIGN=MIDDLE  ALT=\"D%5E2=%280-%28-4%29%29%5E2%2B%281-%28-1%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=%284%29%5E2%2B%282%29%5E2 ALIGN=MIDDLE  ALT=\"D%5E2=%284%29%5E2%2B%282%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=20 ALIGN=MIDDLE  ALT=\"D%5E2=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28D=2%2Asqrt%285%29%29 ALIGN=MIDDLE  ALT=\"highlight%28D=2%2Asqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or approximately,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=4.47 ALIGN=MIDDLE  ALT=\"D=4.47\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );