Describe the boundary lines for two- variableinequalities. Why are the boundary lines for two- variableinequalities with greater than and less represented by dottedlines? Provide examples.
First, define a boundary line and tell where it comes from. Then,describe what the boundary line can tell us about solutions to aninequality. You can also talk about how to know what part of agraph to shade. Finally , talk about the cases where we use eachtype of boundary line. ( solid and dotted/ dashed).
Real - life Relationship: If you have 100 $ available to buy partyfavors ( 3$ per bunch of balloons and 4 $ per bag of candy) thanyou can solve an inequality to find the possibilities . If x = # ofbunches of balloons and y= number of bags of candy then we want tosolve: 3x+ 4y<=100.
Some possible solutions are: no bunches of balloons and 25 bags ofcandy,20 bunches of balloons and 10 bags of candy. There are otherpossibilities!
Challenge: Imagine we have two boundary lines: one solid and onedashed. If they are not parallel is the point where they meetincluded in the solution? Why or why not?
If you are not sure, try an example, such as y < x + 1 and y< = 2x-4. Graph both boundary lines and find the point ofintersection. Then , see if the coordinates satisfy bothinequalities.