6.6 Graphing Inequalities In Two VariablesPresentation Transcript
Graphing Linear Inequalities in Two Variables
Goal 1: Graph a linear inequality in two variables
Goal 2: Model a real life situation with a linear inequality.
Objective- To graph inequalities on the coordinate plane. Recall… Graph n < 3 on a number line. - 3 - 2 - 1 0 1 2 3 4
Half-plane: The region of a graph on one side of a boundary.
Boundary: A boundary of an inequality is a line that separates the coordinate plane into half-planes.
Some Helpful Hints
If the sign is > or < the line is dashed
If the sign is or the line will be solid
When dealing with just x and y.
If the sign > or the shading either goes up or to the right
If the sign is < or the shading either goes down or to the left
Graph y > 3 on the coordinate plane. x y
Graph x - 2 on the coordinate plane. x y
When dealing with slanted lines
If it is > or then you shade above
If it is < or then you shade below the line
Graph y - 3x + 2 on the coordinate plane. x y Boundary Line y = - 3x + 2 m = - 3 b = 2 Test a point not on the line test (0,0) 0 -3(0) + 2 Not true!
Graph y - 3x + 2 on the coordinate plane. x y Instead of testing a point If in y = mx + b form... Shade up Shade down Solid line Dashed line > <
Graph on the coordinate plane. 3x - 4y > 12 - 3x - 3x - 4y > - 3x + 12 - 4 - 4 y < x - 3 m = b = - 3 Boundary Line x y
Problem If you have less than $5.00 in nickels and dimes, find an inequality and sketch a graph to describe how many of each coin you have. Let n = # of nickels Let d = # of dimes 0.05 n + 0.10 d < 5.00 or 5 n + 10 d < 500
5n + 10d < 500 n d 0 50 100 0 0 10 20 30 40 50 60 70 80 90 100 n d 60 50 40 30 20 10 0
To sketch the graph of a linear inequality:
Like a circle on a number line, a dashed line on a coordinate plane indicates that the boundary is not part of the solution set.
Like a dot on a number line, a solid line on a coordinate plane indicates that the boundary is included.