document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=19328>Question 19328</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you tell me how to graph the points of   y=3x-1.  I get confused on the -1 part.  is that negative 1 or minus 1.   thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #9349 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=9349\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello There:\r<BR>\n" );
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document.write( "As far as the -1 goes, there are two ways of looking at it.  It is subtracting a positive 1, or you can say that it is adding a negative 1.\r<BR>\n" );
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document.write( "y = 3*x - (+1)\r<BR>\n" );
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document.write( "y = 3*x + (-1)\r<BR>\n" );
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document.write( "Both interpretations mean the same thing.\r<BR>\n" );
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document.write( "I tend to see it as subtracting a positive 1.\r<BR>\n" );
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document.write( "To graph the solutions to this equation (a line), we need to find the coordinants of two points that satisfy the equation.  Then it's just a matter of plotting these two points and drawing a straight line through them.\r<BR>\n" );
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document.write( "Two easy points to find are the x- and y-intercepts.  The x-intercept occurs when y is zero, and the y-intercept occurs when x is zero.\r<BR>\n" );
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document.write( "Let's find the y-intercept first.  Set x equal to zero.\r<BR>\n" );
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document.write( "y = 3*(0) - 1\r<BR>\n" );
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document.write( "y = -1\r<BR>\n" );
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document.write( "The y-intercept is (0, -1)\r<BR>\n" );
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document.write( "Now we find the x-intercept.  Set y equal to zero.\r<BR>\n" );
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document.write( "0 = 3*x - 1\r<BR>\n" );
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document.write( "Add 1 to both sides.\r<BR>\n" );
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document.write( "0 + 1 = 3*x + 1 - 1\r<BR>\n" );
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document.write( "3*x = 1\r<BR>\n" );
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document.write( "Divide both sides by 3.\r<BR>\n" );
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document.write( "(3/3)*x = 1/3\r<BR>\n" );
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document.write( "x = 1/3\r<BR>\n" );
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document.write( "The x-intercept is (1/3, 0).\r<BR>\n" );
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document.write( "If you find that these two points are too close together to draw an accurate line for your graph, then you can just pick some values for x and substitute them into the equation to get other solutions.\r<BR>\n" );
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document.write( "For example, let's choose 10 for x.\r<BR>\n" );
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document.write( "y = 3*(10) - 1\r<BR>\n" );
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document.write( "y = 30 - 1\r<BR>\n" );
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document.write( "y = 29\r<BR>\n" );
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document.write( "So, the point (10, 29) is also a point on the line.\r<BR>\n" );
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document.write( "~ Mark\r<BR>\n" );
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document.write( " </SPAN>\n" );
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