document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103638>Question 103638</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to solve this problem please help. Graph inequalities\r<BR>\n" );
document.write( "\n" );
document.write( "3x+y&#8804;1<BR>\n" );
document.write( "3(0)+0&#8804;1<BR>\n" );
document.write( " X=1 this is my answer is this correct? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75356 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=75356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.  Solve the equation for y (if necessary).\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2By+%3C=+1 ALIGN=MIDDLE  ALT=\"3x%2By+%3C=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-1+%3C=+y ALIGN=MIDDLE  ALT=\"3x-1+%3C=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3E=+3x-1 ALIGN=MIDDLE  ALT=\"y+%3E=+3x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2.  Graph the equation as if it contained an = sign.<BR>\n" );
document.write( "3.  Draw the line solid if the inequality is   or  <BR>\n" );
document.write( "4.  Draw the line dashed if the inequality is < or > <BR>\n" );
document.write( "5.  Pick a point not on the line to use as a test point.<BR>\n" );
document.write( "     The point (0,0) is a good test point if it is not on<BR>\n" );
document.write( "     the line.<BR>\n" );
document.write( "6.  If the point makes the inequality true, shade that<BR>\n" );
document.write( "     side of the line.  If the point does not make the<BR>\n" );
document.write( "     inequality true, shade the opposite side of the line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now you can graf it and shade everything to the right from the line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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=graphing_linear_equations.solver>Graphing Linear Equations</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>In order to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2Ax-1 ALIGN=MIDDLE  ALT=\"y=3%2Ax-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we only need to plug in two points to draw the line<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So lets plug in some points<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plug in x=-2<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2A%28-2%29-1 ALIGN=MIDDLE  ALT=\"y=3%2A%28-2%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-6-1 ALIGN=MIDDLE  ALT=\"y=-6-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-7 ALIGN=MIDDLE  ALT=\"y=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So here's one point (-2,-7)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-12%2C9%2C+-17%2C+6%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-2%2C-7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C-7%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now lets find another point <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plug in x=-1<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2A%28-1%29-1 ALIGN=MIDDLE  ALT=\"y=3%2A%28-1%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3-1 ALIGN=MIDDLE  ALT=\"y=-3-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4 ALIGN=MIDDLE  ALT=\"y=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So here's another point (-1,-4). Add this to our graph<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-12%2C9%2C+-17%2C+6%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-1%2C-4%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-1%2C-4%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-2%2C-7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C-7%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now draw a line through these points<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-12%2C9%2C+-17%2C+6%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-12-10%2C3%2A%28-12-10%29%2B-1%2C9%2B10%2C3%2A%289%2B10%29%2B-1%29%2C%0D%0A++++blue%28+circle%28+-1%2C-4%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-1%2C-4%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-2%2C-7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-2%2C-7%2C+.1%2C+1.5+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > So this is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2Ax-1 ALIGN=MIDDLE  ALT=\"y=3%2Ax-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (-2,-7) and (-1,-4)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So from the graph we can see that the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F1 ALIGN=MIDDLE  ALT=\"3%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which tells us that in order to go from point to point we have to start at one point and go  up 3 units and to the right 1 units to get to the next point) the y-intercept is (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)and the x-intercept is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.333333333333333 ALIGN=MIDDLE  ALT=\"0.333333333333333\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0)  ,or (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0) <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  We could graph this equation another way. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-1 ALIGN=MIDDLE  ALT=\"b=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >). <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So we have one point (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C11%2C+-11%2C+12%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14-0.05%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now since the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F1 ALIGN=MIDDLE  ALT=\"3%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that in order to go from point to point we can use the slope to do so. So starting at (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we can go up 3 units <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28++600%2C+600%2C+-10%2C11%2C+-11%2C+12%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14-0.05%29+%29%0D%0A++blue%28+arc%28+0%2C+-1%2B%283%2F2%29%2C+2%2C+3%2C+90%2C+270+%29+%29%0D%0A++%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  and to the right 1 units to get to our next point<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28++600%2C+600%2C+-10%2C11%2C+-11%2C+12%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+1%2C2%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+1%2C2%2C+0.14-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14-0.05%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-1%2B%283%2F2%29%2C+2%2C+3%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%281%2F2%29%2C+2%2C+1%2C+2%2C+180%2C+360+%29+%29%0D%0A++%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Now draw a line through those points to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2Ax-1 ALIGN=MIDDLE  ALT=\"y=3%2Ax-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C11%2C+-11%2C+12%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C3%2A%28-10-10%29%2B-1%2C11%2B10%2C3%2A%2811%2B10%29%2B-1%29%2C%0D%0A++++blue%28+circle%28+1%2C2%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+1%2C2%2C+0.14-0.05+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-1%2C+0.14-0.05%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-1%2B%283%2F2%29%2C+2%2C+3%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%281%2F2%29%2C+2%2C+1%2C+2%2C+180%2C+360+%29+%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > So this is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2Ax-1 ALIGN=MIDDLE  ALT=\"y=3%2Ax-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (0,-1) and (1,2)<BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );