document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=989749>Question 989749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the equation in standard form of a perpendicular line that's passes through (5,1)._______y+4=-4(x-2)this equation is the beginning problem u use to answer the problem pls help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #609978 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=609978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We are asked to write an equation in standard form for line that passes through point (5,1),<BR>\n" );
document.write( "and is perpendicular to a line with the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4=-4%28x-2%29 ALIGN=MIDDLE  ALT=\"y%2B4=-4%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The equation of a line can be written in many forms.<BR>\n" );
document.write( "Depending on the information given,<BR>\n" );
document.write( "we may find it easier to start by writing the equation in one or another form.<BR>\n" );
document.write( "Then, if we get the equation of a line in any other form,<BR>\n" );
document.write( "we can always find an equivalent equation in standard form.<BR>\n" );
document.write( "The standard form of the equation of a line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%2BBy=C ALIGN=MIDDLE  ALT=\"Ax%2BBy=C\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > being any real numbers,<BR>\n" );
document.write( "except that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be both zero at the same time.\r<BR>\n" );
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document.write( "If we know a point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28h%2Ck%29 ALIGN=MIDDLE  ALT=\"P%28h%2Ck%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > on a line,<BR>\n" );
document.write( "and we know that the slope of that line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "we can write an equation for that line in point-slope form as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-k=m%28x-h%29 ALIGN=MIDDLE  ALT=\"y-k=m%28x-h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For example, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4=red%28-4%29%28x-2%29 ALIGN=MIDDLE  ALT=\"y%2B4=red%28-4%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%28green%28-4%29%29=red%28-4%29%28x-2%29 ALIGN=MIDDLE  ALT=\"y-%28green%28-4%29%29=red%28-4%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the equation of a line with slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28-4%29 ALIGN=MIDDLE  ALT=\"red%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > that passes through point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%282%2Cgreen%28-4%29%29 ALIGN=MIDDLE  ALT=\"P%282%2Cgreen%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( "For perpendicular lines, if they both have slopes,<BR>\n" );
document.write( "the product of their slopes is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That can also be said as \"their slopes are negative reciprocals (or opposite reciprocals) of each other.\"<BR>\n" );
document.write( "So for a line has a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28-4%29 ALIGN=MIDDLE  ALT=\"red%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "the slope for any perpendicular line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( "So we are looking for the equation of a line with slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29 ALIGN=MIDDLE  ALT=\"%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > that passes through point (5,1).<BR>\n" );
document.write( "The point-slope form for that line (based on that point) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1=%281%2F4%29%28x-5%29 ALIGN=MIDDLE  ALT=\"y-1=%281%2F4%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "From there, we use what we know of algebra to transform that equation into an equivalent equation in standard form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-1=%281%2F4%29%28x-5%29 ALIGN=MIDDLE  ALT=\"y-1=%281%2F4%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28y-1%29=%284%29%281%2F4%29%28x-5%29 ALIGN=MIDDLE  ALT=\"4%28y-1%29=%284%29%281%2F4%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y-4=%281%29%28x-5%29 ALIGN=MIDDLE  ALT=\"4y-4=%281%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y-4=x-5 ALIGN=MIDDLE  ALT=\"4y-4=x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B4y-4=-5 ALIGN=MIDDLE  ALT=\"-x%2B4y-4=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B4y=-5%2B4 ALIGN=MIDDLE  ALT=\"-x%2B4y=-5%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28-x%2B4y=-1%29 ALIGN=MIDDLE  ALT=\"highlight%28-x%2B4y=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x-4y=1%29 ALIGN=MIDDLE  ALT=\"highlight%28x-4y=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( "NOTE: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4y=1 ALIGN=MIDDLE  ALT=\"x-4y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not the only standard form equation for that line.<BR>\n" );
document.write( "It may be the simplest or most elegant answer,<BR>\n" );
document.write( "although some may like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B4y=-1 ALIGN=MIDDLE  ALT=\"-x%2B4y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29x%2By=1%2F4 ALIGN=MIDDLE  ALT=\"%281%2F4%29x%2By=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but multiplying both sides of the equal sign times any non-zero number gives you an equivalent equation,<BR>\n" );
document.write( "so there is an infinite number of equation in standard form for any line.<BR>\n" );
document.write( "In our case, multiplying times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > for example, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x-40y=10 ALIGN=MIDDLE  ALT=\"10x-40y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which is another equivalent equation in standard form. </SPAN>\n" );
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