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# module 10

### math 113 module 10

stepexample
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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