document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=664512>Question 664512</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation of the line in standard form with integer coefficients.\r<BR>\n" );
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document.write( "the line through (8, 3) perpendicular to x + 2y = 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #413766 by </B><A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><B>ReadingBoosters(3246)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><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=413766\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A perpendicular line has a negative reciprocal slope.<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Starting with x+2y=6, convert it into the linear equation format<BR>\n" );
document.write( "x+2y=6<BR>\n" );
document.write( "2y = -x+6<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F2 ALIGN=MIDDLE  ALT=\"6%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the same as y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 3<BR>\n" );
document.write( "...<BR>\n" );
document.write( "The slope of the lines is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "A perpendicular line will have a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F%28-1%2F2%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2F%28-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Where dividing is the same as multiplying the inverse,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F%28-1%2F2%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2F%28-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2A%28-2%2F1%29 ALIGN=MIDDLE  ALT=\"-1%2A%28-2%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "More easily, the negative inverse of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2%29 ALIGN=MIDDLE  ALT=\"-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F1%29+=+2 ALIGN=MIDDLE  ALT=\"%282%2F1%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "Knowing the slope of 2 and using the coordinates (8, 3), solve for y-intercept, b.<BR>\n" );
document.write( "3 = 2(8) + b<BR>\n" );
document.write( "b = 3 - 16 = -13<BR>\n" );
document.write( "...<BR>\n" );
document.write( "The equation of the perpendicular line that passes through (8, 3) is <BR>\n" );
document.write( "y = 2x - 13 :slope-intercept from<BR>\n" );
document.write( "2x - y - 13 = 0 :standard form<BR>\n" );
document.write( ".....<BR>\n" );
document.write( "Red line: y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 3<BR>\n" );
document.write( "Green line: y = 2x - 13<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-2%2C10%2C-20%2C10%2C+%28-1%2F2%29x%2B3%2C+2x-13%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-2%2C10%2C-20%2C10%2C+%28-1%2F2%29x%2B3%2C+2x-13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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