document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146849>Question 146849</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you graph 3x -4y < 12? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108312 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=108312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, change the original inequality into an equation.  Just switch less than with equals.  Then get the original equation into y=mx+b form.  Solve for y, that is. You should get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2F4%29x-3 ALIGN=MIDDLE  ALT=\"y=%283%2F4%29x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The graph of this line looks like this:<BR>\n" );
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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=3+x+%2B+-4+y+=+12 ALIGN=MIDDLE  ALT=\"3+x+%2B+-4+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+=+-3%2F-4 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+-3%2F-4\"   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. 12/3 = 4.</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/-4 = -3.</LI><LI>Slope is -3/-4 = 0.75.</LI><LI> Equation in slope-intercept form: y=0.75*x+-3.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+4-8%2C+4%2B8%2C+-3-8%2C+-3%2B8%2C+0.75%2Ax%2B-3+%29+ ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+4-8%2C+4%2B8%2C+-3-8%2C+-3%2B8%2C+0.75%2Ax%2B-3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
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document.write( "Now since it is less than and not equals, simply dot the line and shade the graph under it.  Then you're done and you have successfully graphed <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C%283%2F4%29x-3 ALIGN=MIDDLE  ALT=\"y%3C%283%2F4%29x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is your original equation in y=mx+b form.  \r<BR>\n" );
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document.write( "If you still need help understanding this concept, go to my lesson on graphing inequalities:<BR>\n" );
document.write( "http://www.algebra.com/algebra/homework/Graphs/Inequalities-Made-Easy.lesson </SPAN>\n" );
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