document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147908>Question 147908</A>: <I><SPAN STYLE=\"word-break: break-all;\"> graph the following inequality on a plane; 3x+4y is less than or equal to 12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108291 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=108291\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First you have to get the equation into y=mx+b form. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y%3C=12 ALIGN=MIDDLE  ALT=\"3x%2B4y%3C=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  First change it to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y=12 ALIGN=MIDDLE  ALT=\"3x%2B4y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Then solve for y and get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283%2F4%29x%2B3 ALIGN=MIDDLE  ALT=\"y=-%283%2F4%29x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Graph that line:<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%2F4 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+-3%2F4\"   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%2B3+%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%2B3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
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document.write( "Now since it was originally <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y%3C=12 ALIGN=MIDDLE  ALT=\"3x%2B4y%3C=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, shade every part of the graph under that line.  Then you're done.\r<BR>\n" );
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document.write( "If you still need help, visit 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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