document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110289>Question 110289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> graph f(x)=-3x-2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80351 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=80351\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What you are asked to graph is the function:<BR>\n" );
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document.write( "f(x) = -3x - 2<BR>\n" );
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document.write( "To get it into a little more conventional form, replace f(x) by y to get:<BR>\n" );
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document.write( "y = -3x - 2<BR>\n" );
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document.write( "One way to graph this is to assign \"convenient\" values to x or y and determine the corresponding<BR>\n" );
document.write( "value of the other variable. Then plot the point. Two points will be enough to draw this<BR>\n" );
document.write( "line graph, and a third point might be a good idea ... just to make sure the three points all <BR>\n" );
document.write( "lie on one straight line. If one of the points is off the line, you know something is wrong.<BR>\n" );
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document.write( "Let's do an easy point ... let's assign x the value of zero. When x equals zero, the term<BR>\n" );
document.write( "-3x is equal to zero and therefore drops from the equation. This reduces the equation to<BR>\n" );
document.write( "y = -2. So when x = 0, then y = -2. This tells you that the point (0, -2) is on the graph.<BR>\n" );
document.write( "(Note that since x = 0, the point is at -2 on the y-axis.)<BR>\n" );
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document.write( "Although it is not as nice, suppose we assign y the value of zero. If we do, the equation<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "0 = -3x - 2<BR>\n" );
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document.write( "We can get rid of the -3x on the right side by adding +3x to both sides. The result of<BR>\n" );
document.write( "this addition is that it changes the equation to:<BR>\n" );
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document.write( "3x = -2<BR>\n" );
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document.write( "Then you can solve for x by dividing both sides by 3 to get:<BR>\n" );
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document.write( "x = -2/3<BR>\n" );
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document.write( "This tells you that the point (-2/3, 0) is on the graph. Note that this point is located at<BR>\n" );
document.write( "-2/3 on the x-axis because points that have zero as their y-value are on the x-axis.<BR>\n" );
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document.write( "Finally, determine one more point. Return to the original equation:<BR>\n" );
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document.write( "y = -3x - 2<BR>\n" );
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document.write( "We can pick any number for x. Suppose we let x = -2. If we substitute -2 for x the equation<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "y = -3(-2) - 2 = +6 - 2 = +4<BR>\n" );
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document.write( "This tells you that the point (-2, +4) is also on the graph. Plot the three points on a<BR>\n" );
document.write( "coordinate system and draw a straight line through them. Your graph should look like this:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C-3x+-+2%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C-3x+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You should be able to see from this graph that the three points we found are all on this line.<BR>\n" );
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document.write( "Hope this helps you to understand one method of determining the graph of a linear equation.<BR>\n" );
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