[tex]\text{For}\ "<"\ \text{and}\ ">"\ \text{is dotted line}.\\\text{For}\ "\leq"\ \text{and}\ "\geq"\ \text{is solid line}.\\\text{For}\ "<"\ \text{and}\ "\leq"\ \text{shaded below a line}.\\\text{For}\ ">"\ \text{and}\ "\geq"\ \text{shaded above a line}.[/tex]
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[tex]3.\\y\leq\dfrac{4}{3}x-1\\\\y=\dfrac{4}{3}x-1\\\\for\ x=0\to y=\dfrac{4}{3}(0)-1=0-1=-1\to(0;\ -1)\\\\for\ x=3\to y=\dfrac{4}{3}(3)-1=4-1=3\to(3,\ 3)\\\\\text{solid line and shaded below a line}[/tex]
[tex]2x+3y>15\qquad\text{subtract 2x from both sides}\\\\3y>-2x+15\qquad\text{divide both sides by 3}\\\\y>-\dfrac{2}{3}x+5\\\\y=-\dfrac{2}{3}x+5\\\\for\ x=0\to y=-\dfrac{2}{3}(0)+5=0+5=5\to(0;\ 5)\\\\for\ x=3\to y=-\dfrac{2}{3}(3)+5=-2+5=3\to(3;\ 3)\\\\\text{dotted line and shaded abowe a line}[/tex]
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[tex]4.\\y<2x-8\\\\y=2x-8\\\\for\ x=0\to y=2(0)-8=0-8=-8\to(0;\ -8)\\\\for\ x=4\to y=2(4)-8=8-8=0\to(4;\ 0)\\\\\text{dotted line and shaded below a line}\\\\\\5x+3y\geq9\qquad\text{subtract 5x from both sides}\\\\3y\geq-5x+9\qquad\text{divide both sides by 3}\\\\y\geq-\dfrac{5}{3}x+3\\\\y=-\dfrac{5}{3}x+3\\\\for\ x=0\to y=-\dfrac{5}{3}(0)+3=0+3=3\to(0;\ 3)\\\\for\ x=3\to y=-\dfrac{5}{3}(3)+3=-5+3=-2\to(3;\ -2)\\\\\text{solid line and shaded above a line}[/tex]
