document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252431>Question 252431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the lines with equations x + 2y = 3  and 3y + Ax = 2 are perpendicular to each other . find the value of A\r<BR>\n" );
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document.write( "a  -6  b  -3/2  c  3/2  d  6  e  22 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184339 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=184339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the 2 equations are in standard form of ax + by = c\r<BR>\n" );
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document.write( "the slope intercept form of these equations would be y = mx + b where m is the slope and b is the y-intercept (value of y when x = 0).\r<BR>\n" );
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document.write( "the easiest thing for you to do is to transform the standard form of these equations into the slope-intercept form of them.\r<BR>\n" );
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document.write( "all you do is solve for y and this happens automatically.\r<BR>\n" );
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document.write( "your first equation is:\r<BR>\n" );
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document.write( "x + 2y = 3\r<BR>\n" );
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document.write( "subtract x from both sides of this equation to get:\r<BR>\n" );
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document.write( "2y = -x + 3\r<BR>\n" );
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document.write( "divide both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "y = -(1/2)*x + (3/2)\r<BR>\n" );
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document.write( "your slope is -(1/2).<BR>\n" );
document.write( "your y-intercept is (3/2).\r<BR>\n" );
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document.write( "your second equation is:\r<BR>\n" );
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document.write( "3y + Ax = 2\r<BR>\n" );
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document.write( "subtract Ax from both sides of this equation to get:\r<BR>\n" );
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document.write( "3y = -Ax + 2\r<BR>\n" );
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document.write( "divide both sides of this equation by 3 to get:\r<BR>\n" );
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document.write( "y = -(A/3)*x + (2/3)\r<BR>\n" );
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document.write( "your slope is -(A/3).<BR>\n" );
document.write( "your y-intercept is (2/3).\r<BR>\n" );
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document.write( "in order for the lines formed by these equations to be perpendicular, the slopes have to be negative reciprocals of each other.\r<BR>\n" );
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document.write( "the two slopes you have to work with are:\r<BR>\n" );
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document.write( "-(1/2) and -(A/3).\r<BR>\n" );
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document.write( "the negative reciprocal of a number is equal to -1 divided by the number.\r<BR>\n" );
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document.write( "the negative reciprocal of -(1/2) = -1/-(1/2).\r<BR>\n" );
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document.write( "this comes out to be equal to 2.\r<BR>\n" );
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document.write( "in order for the lines of these equations to be perpendicular to each other, -(A/3) must be equal to 2 which is the negative reciprocal of -(1/2).\r<BR>\n" );
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document.write( "your equation to solve is:\r<BR>\n" );
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document.write( "-(A/3) = 2\r<BR>\n" );
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document.write( "multiply both sides of this equation by 3 to get:\r<BR>\n" );
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document.write( "-A = 6\r<BR>\n" );
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document.write( "multiply both sides of this equation by (-1) to get:\r<BR>\n" );
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document.write( "A = -6\r<BR>\n" );
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document.write( "your answer is A = -6.\r<BR>\n" );
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document.write( "your original equations were:\r<BR>\n" );
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document.write( "x + 2y = 3 and 3y + Ax = 2 \r<BR>\n" );
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document.write( "replace A with -6 to get:\r<BR>\n" );
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document.write( "x + 2y = 3 and 3y - 6x = 2\r<BR>\n" );
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document.write( "to graph these equations, we need to solve for y which automatically puts them into the slope-intercept form.\r<BR>\n" );
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document.write( "we get:\r<BR>\n" );
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document.write( "y = -(1/2)*x + (3/2) and y = (6/3)*x + (2/3)\r<BR>\n" );
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document.write( "the second equation simplifies to:\r<BR>\n" );
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document.write( "y = 2*x + (2/3) because 6/3 is the same as 2.\r<BR>\n" );
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document.write( "the graph of these equations looks like this:\r<BR>\n" );
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document.write( "y = -(1/2)*x + (3/2) crosses the y-axis at (3/2) = 1.5.   This graph slopes down from left to right.\r<BR>\n" );
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document.write( "y = 2*x + (2/3) crosses the y-axis at (2/3) = .66666667.   This graph slopes up from left to right.\r<BR>\n" );
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