document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=262695>Question 262695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of the line that contains the point (1,0) and is perpendicular to 2x+y=4. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193495 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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=193495\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find an equation of the line that contains the point (1,0) and is perpendicular to 2x+y=4.\r<BR>\n" );
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document.write( "First you must know that lines perpendicular to on another have a slopes that are negative reciprocals of one another.  For example, if a slope of a line is 4, a line perpendicular to that line will have a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F4 ALIGN=MIDDLE  ALT=\"%28-1%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   If you were to multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F1 ALIGN=MIDDLE  ALT=\"4%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F4 ALIGN=MIDDLE  ALT=\"%28-1%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > you would get -1.   Negative reciprocals, when multiplied, will result in the number -1. :-)\r<BR>\n" );
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document.write( "If lines have the SAME slope, they are parallel.\r<BR>\n" );
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document.write( "Now that we have those facts, let's look at the line you are given.  The equation for the line you are given is:  2x + y = 4.   If you were to put this line into the slope intercept equation of a line, which is y = mx + b, then you'd see the slope immediately.  In the equation y = mx + b, the slope is \"m\".  \r<BR>\n" );
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document.write( "SO let's put your line into the y = mx + b format, which means that we will solve for y.  Here goes:\r<BR>\n" );
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document.write( "2x + y = 4 (your original equation)<BR>\n" );
document.write( "y = 4 - 2x (subtract 2x from both sides to isolate the y)\r<BR>\n" );
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document.write( "y = -2x + 4  (rewrite the equation so that the slope is clear to you)<BR>\n" );
document.write( "y = mx + b\r<BR>\n" );
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document.write( "Looking above, can you see that m = -2?   SO... if our slope is equal to -2, (which is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%2F1 ALIGN=MIDDLE  ALT=\"%28-2%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > the negative reciprocal to that number is going to be:  <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;\" >.  (I just flipped the fraction and changed the sign).\r<BR>\n" );
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document.write( "Our new line must have a slope of <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;\" > and it must go thru point (1,0). \r<BR>\n" );
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document.write( "When we know a point on the line [in this case the point is (1,0)] and we know the slope, [in this case, we want a slope of <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;\" >]we should use the POINT SLOPE equation of a line, which is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+y%5B1%5D%29 ALIGN=MIDDLE  ALT=\"%28y+-+y%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%28x+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m%28x+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Now that we know the formula, we just fill in the info we are given.\r<BR>\n" );
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document.write( "We want this:  m = <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;\" >   thru point  (1,0).  <BR>\n" );
document.write( "Let's plug that into the point slope equation of a line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+y%5B1%5D%29 ALIGN=MIDDLE  ALT=\"%28y+-+y%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%28x+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m%28x+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (point slope equation of a line)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+0%29 ALIGN=MIDDLE  ALT=\"%28y+-+0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28x+-+1%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28x+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (point slope equation with slope of <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;\" > and point (1,0) plugged in)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29x+-+1%2F2 ALIGN=MIDDLE  ALT=\"%281%2F2%29x+-+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (distributed <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;\" > to the x and distributed  <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;\" > to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29 ALIGN=MIDDLE  ALT=\"%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now we have our equation of a line that is perpendicular to the first equation you were given.    y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29x+-+1%2F2 ALIGN=MIDDLE  ALT=\"%281%2F2%29x+-+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I hope this helps you. :-) </SPAN>\n" );
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