document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112353>Question 112353</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0471530123/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> How far is the point (5,3) from the line y = 4x+1?\r<BR>\n" );
document.write( "\n" );
document.write( "Hint: the point must lie on a line perpendicular to the given line.<BR>\n" );
document.write( "Use the distance formula for two points in a plane. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82001 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=82001\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, find the line perpendicular to your original line that goes through the point (5,3). <BR>\n" );
document.write( "Perpendicular lines have slopes that follow this relationship,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5Dm%5B2%5D=-1 ALIGN=MIDDLE  ALT=\"m%5B1%5Dm%5B2%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Their slopes are negative reciprocals.<BR>\n" );
document.write( "Your original line slope is 4. <BR>\n" );
document.write( "Your perpendicular line slope is then (-1/4).<BR>\n" );
document.write( "Using the point-slope form of the line, your perpendicular line is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%28x-x%5B1%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-3=%28-1%2F4%29%28x-5%29 ALIGN=MIDDLE  ALT=\"y-3=%28-1%2F4%29%28x-5%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%2F4%29x%2B5%2F4%2B3 ALIGN=MIDDLE  ALT=\"y=%28-1%2F4%29x%2B5%2F4%2B3\"   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%2F4%29x%2B5%2F4%2B12%2F4 ALIGN=MIDDLE  ALT=\"y=%28-1%2F4%29x%2B5%2F4%2B12%2F4\"   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%2F4%29x%2B17%2F4 ALIGN=MIDDLE  ALT=\"y=%28-1%2F4%29x%2B17%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+4x%2B1%2C+%28-1%2F4%29x%2B17%2F4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+4x%2B1%2C+%28-1%2F4%29x%2B17%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Now that you have the equation for the two lines, you can find the intersection point where the two lines meet. <BR>\n" );
document.write( "From there you can calculate the distance from the intersection point to (5,3) to get the final answer.<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4x%2B1 ALIGN=MIDDLE  ALT=\"y+=+4x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F4%29x%2B17%2F4 ALIGN=MIDDLE  ALT=\"y=%28-1%2F4%29x%2B17%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute equation 1 into equation 2 and solve for x.<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F4%29x%2B17%2F4 ALIGN=MIDDLE  ALT=\"y=%28-1%2F4%29x%2B17%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B1=%28-1%2F4%29x%2B17%2F4 ALIGN=MIDDLE  ALT=\"4x%2B1=%28-1%2F4%29x%2B17%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%2F4%29x%2B%281%2F4%29x=17%2F4-1 ALIGN=MIDDLE  ALT=\"%2816%2F4%29x%2B%281%2F4%29x=17%2F4-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2817%2F4%29x=17%2F4-4%2F4 ALIGN=MIDDLE  ALT=\"%2817%2F4%29x=17%2F4-4%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2817%2F4%29x=13%2F4 ALIGN=MIDDLE  ALT=\"%2817%2F4%29x=13%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13%2F17 ALIGN=MIDDLE  ALT=\"x=13%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From 1,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4x%2B1 ALIGN=MIDDLE  ALT=\"y+=+4x%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+=+4%2813%2F17%29%2B1 ALIGN=MIDDLE  ALT=\"y+=+4%2813%2F17%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+=+52%2F17%2B17%2F17 ALIGN=MIDDLE  ALT=\"y+=+52%2F17%2B17%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+69%2F17 ALIGN=MIDDLE  ALT=\"y+=+69%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now you have found the intersection point.<BR>\n" );
document.write( "Use the distance formula to find the distance between the intersection point and the point (5,3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2 ALIGN=MIDDLE  ALT=\"D%5E2=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%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=%2813%2F17-5%29%5E2%2B%2869%2F17-3%29%5E2 ALIGN=MIDDLE  ALT=\"D%5E2=%2813%2F17-5%29%5E2%2B%2869%2F17-3%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=%2813%2F17-85%2F17%29%5E2%2B%2869%2F17-51%2F17%29%5E2 ALIGN=MIDDLE  ALT=\"D%5E2=%2813%2F17-85%2F17%29%5E2%2B%2869%2F17-51%2F17%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=%28-72%2F17%29%5E2%2B%2818%2F17%29%5E2 ALIGN=MIDDLE  ALT=\"D%5E2=%28-72%2F17%29%5E2%2B%2818%2F17%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=%285184%2F289%29%2B%28324%2F289%29 ALIGN=MIDDLE  ALT=\"D%5E2=%285184%2F289%29%2B%28324%2F289%29\"   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=%285508%2F289%29 ALIGN=MIDDLE  ALT=\"D%5E2=%285508%2F289%29\"   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=%285508%2F289%29 ALIGN=MIDDLE  ALT=\"D%5E2=%285508%2F289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=4.37 ALIGN=MIDDLE  ALT=\"D=4.37\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );