document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142934>Question 142934</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Explain what the basic method for graphing a linear equation. Provide an example of a linear equation and show how you would graph your equation. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108323 by </B><A HREF=/tutors/aboutme.mpl?userid=mangopeeler07><B>mangopeeler07(462)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mangopeeler07><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=108323\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is a solution that I posted earlier today, explaning how to graph a line. I used the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2%2F3%29x+%2B+4 ALIGN=MIDDLE  ALT=\"y+=+%28-2%2F3%29x+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > in this example:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Start with an empty graph. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2%2F3%29x+%2B+4 ALIGN=MIDDLE  ALT=\"y+=+%28-2%2F3%29x+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is already in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > (line)form.  m is the slope, and b is the y intercept (what y is when x is zero). b is where you start on the y axis with your line, in this case 4.  plot one point on (0,4).  -2/3 is the slope.  This is also known as rise over run.  -2 is the change of the y axis, and 3 is the change on the x axis.  It can also be that 2 is the change on the y axis and -3 is the change on the x axis.  It doesn't matter, same line.  I'll explain what I mean by \"change\" while we plot this line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To plot the line, just start at (0,4), the point you've already plotted, and move in one of these two directions:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--to the right 3 and down 2 (over and over to plot points) or <BR>\n" );
document.write( "--to the left 3 and up 2 (over and over to plot points)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "These are the changes in the x and y axis.  x moves right or left depending on whether the denominator of the slope is positive or negative, and y moves up or down depending on whether the numerator of the slope is positive or negative. (So if the slope is negative, the negative can go on either the denominator or the numerator.)\r<BR>\n" );
document.write( "\n" );
document.write( "When you are done, your graph should look like this:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=describe_linear_equation.solver>DESCRIBE a linear EQUATION: slope, intercepts, etc</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+x+%2B+3+y+=+12 ALIGN=MIDDLE  ALT=\"2+x+%2B+3+y+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > describes a sloping line. For any <BR>\n" );
document.write( "  equation ax+by+c = 0, slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Fb+=+-2%2F3 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<UL><LI>X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x =  c/a. 12/2 = 6.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 12/3 = 4.</LI><LI>Slope is -2/3 = -0.666666666666667.</LI><LI> Equation in slope-intercept form: y=-0.666666666666667*x+4.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+6-8%2C+6%2B8%2C+4-8%2C+4%2B8%2C+-0.666666666666667%2Ax%2B4+%29+ ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+6-8%2C+6%2B8%2C+4-8%2C+4%2B8%2C+-0.666666666666667%2Ax%2B4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
document.write( "</TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now you have successfully graphed a line. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );