document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=17311>Question 17311</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3x-6y=9 You have to solve for x and y. Then graph the two points on a graph. Then name the slope and y intercept.\r<BR>\n" );
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document.write( "Thanks in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #8340 by </B><A HREF=/tutors/aboutme.mpl?userid=mmm4444bot><B>mmm4444bot(95)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mmm4444bot><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=8340\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi There:\r<BR>\n" );
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document.write( "I will show you how to solve the equation for x and y, but it's not necessary if you only need to find the coordinates of two points.\r<BR>\n" );
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document.write( "In fact, finding the coordinates of two points does not require solving the equation at all.  The two easiest points to find are the x- and y-intercepts.\r<BR>\n" );
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document.write( "The x-intercept occurs when y = 0.\r<BR>\n" );
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document.write( "The y-intercept occurs when x = 0.\r<BR>\n" );
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document.write( "Substitute 0 for y:\r<BR>\n" );
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document.write( "3x - 6(0) = 9\r<BR>\n" );
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document.write( "3x = 9\r<BR>\n" );
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document.write( "x = 3\r<BR>\n" );
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document.write( "The x-intercept is at the point (3, 0).\r<BR>\n" );
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document.write( "Substitute 0 for x:\r<BR>\n" );
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document.write( "3(0) - 6y = 9\r<BR>\n" );
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document.write( "-6y = 9\r<BR>\n" );
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document.write( "y = -9/6\r<BR>\n" );
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document.write( "y = -3/2\r<BR>\n" );
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document.write( "The y-intercept is at the point (0, -3/2).\r<BR>\n" );
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document.write( "To solve the equation for x means that we want to isolate the variable x on one side of the equals sign and move everything else to the other side.\r<BR>\n" );
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document.write( "Start by isolating 3x first; move the -6y term to the other side by adding it to both sides of the equation.\r<BR>\n" );
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document.write( "3x - 6y + 6y = 9 + 6y\r<BR>\n" );
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document.write( "3x = 9 + 6y\r<BR>\n" );
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document.write( "Now we solve for x by dividing both sides by 3.\r<BR>\n" );
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document.write( "(3x)/3 = (9 + 6y)/3\r<BR>\n" );
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document.write( "x = 9/3 + (6y)/3\r<BR>\n" );
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document.write( "x = 3 + 2y\r<BR>\n" );
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document.write( "We do something similar to solve the equation for y.\r<BR>\n" );
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document.write( "Move the 3x term to the other side to isolate -6y.  We do this by subtracting 3x from both sides.\r<BR>\n" );
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document.write( "3x - 3x - 6y = 9 - 3x\r<BR>\n" );
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document.write( "-6y = 9 - 3x\r<BR>\n" );
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document.write( "Divide both sides by -6 to solve for y.\r<BR>\n" );
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document.write( "(-6y)/(-6) = (9 - 3x)/(-6)\r<BR>\n" );
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document.write( "y = 9/(-6) - (3x)/(-6)\r<BR>\n" );
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document.write( "y = -3/2 + x/2\r<BR>\n" );
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document.write( "This last equation is usually written like this:\r<BR>\n" );
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document.write( "y = (1/2)*x - 3/2\r<BR>\n" );
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document.write( "and it is called the slope-intercept form of the equation for the line.  It is called this because it shows at a quick glance what the slope is and what the y-intercept is.\r<BR>\n" );
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document.write( "It's this form:  y = m*x + b\r<BR>\n" );
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document.write( "where m is the slope and b is the y-intercept.\r<BR>\n" );
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document.write( "y = (1/2)*x - 3/2\r<BR>\n" );
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document.write( "Solving the equation for y shows us that m = 1/2 and b = -3/2.\r<BR>\n" );
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document.write( "~ Mark<BR>\n" );
document.write( " </SPAN>\n" );
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