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# module 10

### math 113 module 10

step | example |
---|---|

The first step is to graph the boundary line of the problem. | x+y>7 Plot the points that make x+y=7 (7,0),(0,7) |

The second step is to determine weather the boundary line is going to be solid or dashed. | The line will be solid if the problem states x+y is greater/less than OR equal to a number. If the equation states that x+y is greater/less than, the boundary line on the graph will be dashed. |

The third step is to chose two points, on the graph, that satisfy the inequality. make sure the test point is not on the boundary line. | x+y>7 use test point (0,0) on the graph to satisfy the inequality. x+y>7, 0+0>7, since 0 is not greater than 7, shade the part of the graph that DOES NOT contain the test point (0,0). |

X+5Y<3 solve for x by substituting 0 for Y. (3,0) solve for y by substituting -2 for X. (-2,1) chose a test point to satisfy the inequality. (0,0) | Boundary line is a dashed line through the following points (3,0),(-2,1). Test point (0,0) 0+5(0)<3. 0<3 is true. Shade portion of graph that contains test point (0,0) |

If the inequality states that a variable is <,> the boundary line should be a _________ line? | The boundary line should be a dashed line |

If the inequality states that the variable is greater/less than OR equal to, the boundary line should be a _______ line? | The boundary line should be a solid line. |

X<-1 | Plot the point -1 on the graph to establish a dashed, vertical, boundary line for the equation. use the test point (0,0) 0<-1 is not a true statement so shade the half of the graph that does not contain the test point (0,0) |

Graph the solution of the system of linear inequalities. Y>X+3 Y>5-X | The first step is to graph the points of each inequality to establish 2 separate boundary lines. Y>X+3 is Y=X+3 Graph (0,3)(-3,0) dashed line Y>5-X is Y=5-X Graph (0,5)(5,0) dashed line. Chose a test point. (0,0). Shaded area is overlap of both lines. |

When graphing the solution of the system of linear inequalities, the shaded portion of the graph should fall_______? | The shaded portion of the graph should fall between the overlapping portion of the two boundary lines that correspond to the test point used for each. |

3X-2Y>-8 should have a ______ boundary line? | The boundary line should be dashed a dashed line. the greater than is always a dashed line. |

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