document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=463036>Question 463036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which choice is the equation of a line that passes through the point (–2, 8) and is perpendicular to the line represented by this equation?\r<BR>\n" );
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document.write( "5x &#8722; 2y = &#8722;10\r<BR>\n" );
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document.write( " A. 2x&#8722; 5y = 26 <BR>\n" );
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document.write( " B. 5x + 2y = 10 <BR>\n" );
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document.write( " C. 2x + 5y = 36 <BR>\n" );
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document.write( " D. &#8722;2x + 5y = &#8722;13 <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317336 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=317336\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you start with the equation of 5x - 2y = -10.\r<BR>\n" );
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document.write( "if you subtract 5x from both sides of this equation you get -2y = -5x - 10.\r<BR>\n" );
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document.write( "if you divide both sides of this equation by -2, you get y = (5/2)x + 5.\r<BR>\n" );
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document.write( "your slope is (5/2)\r<BR>\n" );
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document.write( "The slope of a perpendicular line would be equal to the negative reciprocal of (5/2) which would be equal to -(2/5).\r<BR>\n" );
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document.write( "the line would be passing through the point (x,y) = (-2,8).\r<BR>\n" );
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document.write( "you can use the point slope form of the equation to derive the equation as follows:\r<BR>\n" );
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document.write( "the point slope form is y-y1 = m*(x-x1)\r<BR>\n" );
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document.write( "(x1,y1) is the point that the line is passing through.\r<BR>\n" );
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document.write( "you get y - 8 = -(2/5) * (x + 2)\r<BR>\n" );
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document.write( "this becomes y - 8 = -(2/5)*x - (4/5)\r<BR>\n" );
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document.write( "add 8 to both sides of this equation and you get y = -(2/5)x + 8 - (4/5) which becomes y = (-2/5)x + (36/5)\r<BR>\n" );
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document.write( "multiply both sides of this equation by 5 and you get 5y = -2x + 36.\r<BR>\n" );
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document.write( "add 2x to both sides of this equation and you get 2x + 5y = 36.\r<BR>\n" );
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document.write( "that matches selection c.\r<BR>\n" );
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document.write( "there might be a simpler way of looking at this.\r<BR>\n" );
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document.write( "your equation is 5x - 2y = -10\r<BR>\n" );
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document.write( "the general form of this equation in standard form is ax + by = c\r<BR>\n" );
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document.write( "this means that a is the coefficient of x and b is the coefficient of y.\r<BR>\n" );
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document.write( "the slope is given by the formula -a/b\r<BR>\n" );
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document.write( "in your equation, a is 5 and b is -2.\r<BR>\n" );
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document.write( "the slope is therefore -5/-2 which is equal to 5/2.\r<BR>\n" );
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document.write( "the line perpendicular to this would have a slope that is the negative reciprocal of that, so the slope of the perpendicular line has to be -2/5.\r<BR>\n" );
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document.write( "plug this slope back into the standard form of the equation of ax + by = c and you get 2x + 5y = c because -a is equal to -2 which makes a = 2, and b = 5\r<BR>\n" );
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document.write( "because the equation passed through the point (-2,8), you then simply replace x with -2 and y with 8 to get 2(-2) + 5*8 = -4 + 40 = 36.\r<BR>\n" );
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document.write( "this makes the value of c = 36 and your equation becomes 2x + 5y = 36.\r<BR>\n" );
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document.write( "this also leads to selection c.\r<BR>\n" );
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document.write( "you can do it either way.\r<BR>\n" );
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document.write( "converting to slope intercept form (y = mx + b) where m is the slope and b is the y intercept is how its normally done, but if you are working from the standard form of the equation and remember that slope is equal to -b/a, then you can derive it the alternate way as well.\r<BR>\n" );
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