\r\n" );
document.write( "First we plot the boundary, whose equation is just like the inequality except\r\n" );
document.write( "the ≤ is replaced by =.\r\n" );
document.write( "\r\n" );
document.write( "We plot the line whose equation is\r\n" );
document.write( "\r\n" );
document.write( "y=2x+2 \r\n" );
document.write( "\r\n" );
document.write( "by getting two points on the line. \r\n" );
document.write( "\r\n" );
document.write( " x|y\r\n" );
document.write( " 0|?\r\n" );
document.write( " ?|0\r\n" );
document.write( "\r\n" );
document.write( "if x=0, we substitute 0 for x:\r\n" );
document.write( "\r\n" );
document.write( "y=2(0)+2\r\n" );
document.write( "y=2\r\n" );
document.write( "\r\n" );
document.write( " x|y\r\n" );
document.write( " 0|2\r\n" );
document.write( " ?|0\r\n" );
document.write( "\r\n" );
document.write( "if y=0, we substitute 0 for y\r\n" );
document.write( "\r\n" );
document.write( " 0=2x+2\r\n" );
document.write( "-2=2x\r\n" );
document.write( "-1=x\r\n" );
document.write( "\r\n" );
document.write( " x|y\r\n" );
document.write( " 0|2\r\n" );
document.write( "-1|0\r\n" );
document.write( "\r\n" );
document.write( "So we plot the points (0,2) and (-1,0)\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "We draw a SOLID line through those two points, SOLID, not DOTTED,\r\n" );
document.write( "because the inequality is ≤ and not < . Since ≤ includes =, the\r\n" );
document.write( "graph will contain its boundary line as well as the shaded part.\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We pick a test point which is NOT on the line to substitute in the \r\n" );
document.write( "original inequality to see which side of the line the solutions lie \r\n" );
document.write( "on. The easiest test point to pick is (0,0), the origin and we can \r\n" );
document.write( "pick it as long as the line does not pass through the origin. The\r\n" );
document.write( "line does not pass through the origin so we will substitute (0,0)\r\n" );
document.write( "in the inequality:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "y≤2x+2 \r\n" );
document.write( "0≤2(0)+2\r\n" );
document.write( "0≤2\r\n" );
document.write( "\r\n" );
document.write( "This is true, so the test point (0,0) is a solution and so all the\r\n" );
document.write( "solutions will be on the same side of the line that the origin is on.\r\n" );
document.write( "The origin is on the lower right side of the line so we will shade\r\n" );
document.write( "that side of the line:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "That graph is the answer!\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" );
document.write( "\n" );
document.write( "
\n" );
document.write( " \n" );
document.write( "![\"\"](\"/images/stars/stars-13.gif\")
