document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=715656>Question 715656</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have no idea how to solve this problem.<BR>\n" );
document.write( "It says graph x+y<-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #439565 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=439565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To graph an inequality you first graph the boundary line, making it a solid line if the inequality sign includes \"or equal\", or a dashed lined, if it's just greater than, or just lesser than.<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3C-1 ALIGN=MIDDLE  ALT=\"x%2By%3C-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > you will graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=-1 ALIGN=MIDDLE  ALT=\"x%2By=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a dashed line.<BR>\n" );
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document.write( "After graphing the boundary line, you color (or shade) the side of the line that represents all the solutions to the inequality.<BR>\n" );
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document.write( "You could solve for y, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3C-1 ALIGN=MIDDLE  ALT=\"x%2By%3C-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C-x-1 ALIGN=MIDDLE  ALT=\"y%3C-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and color as solution all the points below the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x-1 ALIGN=MIDDLE  ALT=\"y=-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "because for each x, the points below the line have a y value that is less that the y on the line.<BR>\n" );
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document.write( "HOW TO GRAPH A LINE:<BR>\n" );
document.write( "If you know two points on the line, you just plot those points and connect them with a straight line.<BR>\n" );
document.write( "I see that the line with the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=-1 ALIGN=MIDDLE  ALT=\"x%2By=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > passes through points (0,-1) and (-1,0) because<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > indicating that (0,-1) is a point on the line, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > indicating that (-1,0) is a point on the line.<BR>\n" );
document.write( "I can use those points to graph the line.<BR>\n" );
document.write( "If you have the equation in the slope-intercept form, a in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x-1 ALIGN=MIDDLE  ALT=\"y=-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , you can use the y-intercept for one point, and the slope to go from one point to another.<BR>\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > at the end of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x-1 ALIGN=MIDDLE  ALT=\"y=-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > tells you that the y-intercept is <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( "meaning that the line crosses the y-axis at point (0,-1).<BR>\n" );
document.write( "The line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x-1 ALIGN=MIDDLE  ALT=\"y=-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ).<BR>\n" );
document.write( "A slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > means that as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > increases by 1, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > increases by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (meaning that it decreases by 1.<BR>\n" );
document.write( "So from (0,-1) you would go to (1,-2) and then to (2,-3), and so on.<BR>\n" );
document.write( "Reversing direction, you could go from (0,-1) to (-1,0) and then to (-2,1), and so on.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-5%2C5%2C%0D%0Agrid%281%29%2C%0D%0Ablue%28line%28-5%2C4%2C5%2C-6%29%29%2Cblue%28circle%280%2C-1%2C0.2%29%29%2C+green%28circle%28-1%2C0%2C0.2%29%29%2C%0D%0Agreen%28circle%28-2%2C1%2C0.2%29%29%2Cgreen%28circle%281%2C-2%2C0.2%29%29%2C%0D%0Agreen%28circle%282%2C-3%2C0.2%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "HOW TO DECIDE WHICH SIDE OF THE LINE IS THE SOLUTION:<BR>\n" );
document.write( "If your inequality is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C-x-1 ALIGN=MIDDLE  ALT=\"y%3C-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > the lesser than sign tells you that the solution is all the points below the line with equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x-1 ALIGN=MIDDLE  ALT=\"y=-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If your inequality is something like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3C-1 ALIGN=MIDDLE  ALT=\"x%2By%3C-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , you can figure out which side is the solution by using a test point that is not on the line.<BR>\n" );
document.write( "You would chose a test point that makes calculations easy.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%3C-1 ALIGN=MIDDLE  ALT=\"x%2By%3C-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, I would chose point (0,0), the origin.<BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , I see that the origin is not part of the solution because<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=0%2B0=0 ALIGN=MIDDLE  ALT=\"x%2By=0%2B0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not lesser than <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( "So I know that the solution is the side of line that does not contain the origin.<BR>\n" );
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document.write( "YOUR SOLUTION<BR>\n" );
document.write( "is the green shaded area, all the way to the dashed blue line. but not including that line. (We draw the boundary line as a dashed line to show that the points of that line are not part of the solution).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-5%2C5%2C%0D%0Agrid%280%29%2C%0D%0Ablue%28line%28-5%2C4%2C-4.67%2C3.67%29%29%2Cblue%28line%28-4.33%2C3.33%2C-4%2C3%29%29%2Cblue%28line%28-3.67%2C2.67%2C-3.33%2C2.33%29%29%2C%0D%0Ablue%28line%28-3%2C2%2C-2.67%2C1.67%29%29%2Cblue%28line%28-2.33%2C1.33%2C-2%2C1%29%29%2Cblue%28line%28-1.67%2C0.67%2C-1.33%2C0.33%29%29%2C%0D%0Ablue%28line%28-1%2C0%2C-0.67%2C-0.33%29%29%2Cblue%28line%28-0.33%2C-0.67%2C0%2C-1%29%29%2Cblue%28line%280.33%2C-1.33%2C0.67%2C-1.67%29%29%2C%0D%0Ablue%28line%281%2C-2%2C1.33%2C-2.33%29%29%2Cblue%28line%281.67%2C-2.67%2C2%2C-3%29%29%2Cblue%28line%282.33%2C-3.33%2C2.67%2C-3.67%29%29%2C%0D%0Ablue%28line%283%2C-4%2C3.33%2C-4.33%29%29%2Cblue%28line%283.67%2C-4.67%2C4%2C-5%29%29%2C%0D%0Agreen%28line%28-4.8%2C3.8%2C-5.8%2C2.8%29%29%2Cgreen%28line%28-4.47%2C3.47%2C-5.47%2C2.47%29%29%2C%0D%0Agreen%28line%28-4.13%2C3.13%2C-5.13%2C2.13%29%29%2C%0D%0Agreen%28line%28-3.8%2C2.8%2C-5.8%2C0.8%29%29%2Cgreen%28line%28-3.47%2C2.47%2C-5.47%2C0.47%29%29%2C%0D%0Agreen%28line%28-3.13%2C2.13%2C-5.13%2C0.13%29%29%2Cgreen%28line%28-2.8%2C1.8%2C-5.8%2C-1.2%29%29%2C%0D%0Agreen%28line%28-2.47%2C1.47%2C-5.47%2C-1.53%29%29%2Cgreen%28line%28-2.13%2C1.13%2C-5.13%2C-1.87%29%29%2C%0D%0Agreen%28line%28-1.8%2C0.8%2C-5.8%2C-3.2%29%29%2Cgreen%28line%28-1.47%2C0.47%2C-5.47%2C-3.53%29%29%2C%0D%0Agreen%28line%28-1.13%2C0.13%2C-5.13%2C-3.87%29%29%2Cgreen%28line%28-0.8%2C-0.2%2C-4.8%2C-4.2%29%29%2C%0D%0Agreen%28line%28-0.47%2C-0.53%2C-4.47%2C-4.53%29%29%2Cgreen%28line%28-0.13%2C-0.87%2C-4.13%2C-4.87%29%29%2C%0D%0Agreen%28line%280.2%2C-1.2%2C-3.8%2C-5.2%29%29%2Cgreen%28line%280.53%2C-1.53%2C-3.47%2C-5.53%29%29%2C%0D%0Agreen%28line%280.87%2C-1.87%2C-3.13%2C-5.87%29%29%2Cgreen%28line%281.2%2C-2.2%2C-1.8%2C-5.2%29%29%2C%0D%0Agreen%28line%281.53%2C-2.53%2C-1.47%2C-5.53%29%29%2Cgreen%28line%281.87%2C-2.87%2C-1.13%2C-5.87%29%29%2C%0D%0Agreen%28line%282.87%2C-3.87%2C0.87%2C-5.87%29%29%2Cgreen%28line%283.87%2C-4.87%2C1.87%2C-5.87%29%29%2C%0D%0Agreen%28line%282.2%2C-3.2%2C0.2%2C-5.2%29%29%2Cgreen%28line%282.53%2C-3.53%2C0.53%2C-5.53%29%29%2C%0D%0Agreen%28line%283.2%2C-4.2%2C1.2%2C-6.2%29%29%2Cgreen%28line%283.53%2C-4.53%2C1.53%2C-6.53%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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