document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=216692>Question 216692</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the distance between P(7,-4) and the line with equation x-3y+5=0.round to the nearest tenth </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163600 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=163600\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the distance between P(7,-4) and the line with equation x-3y+5=0.<BR>\n" );
document.write( "round to the nearest tenth<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the slope of the given equation<BR>\n" );
document.write( "x - 3y + 5 = 0<BR>\n" );
document.write( "-3y = -x - 5<BR>\n" );
document.write( "Multiply eq by -1 to get rid of all those negatives<BR>\n" );
document.write( "3y = x + 5<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F3 ALIGN=MIDDLE  ALT=\"5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "The slope: m1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the slope of a line perpendicular (m2) to this equation<BR>\n" );
document.write( "m1 * m2 = -1; the relationship of slopes of perpendicular lines<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >m2 = -1<BR>\n" );
document.write( "m2 = -1*3<BR>\n" );
document.write( "m2 = -3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the equation of the perpendicular line that passes thru P(7,-4)<BR>\n" );
document.write( "Use the point/slope formula y - y1 = m(x - x1)<BR>\n" );
document.write( "y -(-4) = -3(x - 7)<BR>\n" );
document.write( "y + 4 = -3x + 21<BR>\n" );
document.write( "y = -3x + 21 - 4<BR>\n" );
document.write( "y = -3x + 17 is the equation of the perpendicular line<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the value of x common to both equations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F3 ALIGN=MIDDLE  ALT=\"5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -3x + 17<BR>\n" );
document.write( "multiply both sides by 3<BR>\n" );
document.write( "x + 5 = -9x + 51<BR>\n" );
document.write( "x + 9x = 51 - 5<BR>\n" );
document.write( "10x = 46<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=46%2F10 ALIGN=MIDDLE  ALT=\"46%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 4.6<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the value for y:<BR>\n" );
document.write( "y = -3(4.6) + 17<BR>\n" );
document.write( "y = -13.8 + 17<BR>\n" );
document.write( "y = +3.2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the distance from points x1 = 7, y1 =-4 and x2 = 4.6, y2 =3.2<BR>\n" );
document.write( "The distance formula d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using our point values<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%284.6-7%29%5E2+%2B+%283.2-%28-4%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%284.6-7%29%5E2+%2B+%283.2-%28-4%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28-2.4%29%5E2+%2B+%287.2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28-2.4%29%5E2+%2B+%287.2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285.76+%2B+51.84%29 ALIGN=MIDDLE  ALT=\"sqrt%285.76+%2B+51.84%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2857.6%29 ALIGN=MIDDLE  ALT=\"sqrt%2857.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = 7.589 ~ 7.6 dist between P(7,-4) and Eq x - 3y + 5 = 0.<BR>\n" );
document.write( " </SPAN>\n" );
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