kristie ferrentino. 1. find and graph the solution set of the inequality. 2. determine the equation...
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Kristie Ferrentino
Graphing Linear Inequalities
in Two Variables
ADMIT TICKET
1. Find and graph the solution set of the inequality.
2. Determine the equation of a line that passes through the point (2,6) and has a slope of 5.
162)2(4 xx
OBJECTIVE
Students will be able to demonstrate their understanding of how to solve linear inequalities in two variables by graphing linear inequalities in two variables.
GRAPH LINEAR INEQUALITIES
Linear inequality graph: is a set of points in a coordinate plane that represent all of the possible solutions of that inequality We represent the boundary line of the
inequality by drawing the function represented in the inequality
Boundary Line: separates the coordinate plane into regions
GRAPHING LINEAR INEQUALITIES
Inequality Type of Line Shaded Region
> (greater than) Above
< (less than) Below
≥ (greater than and/or equal to) Above
≤ (less than and/or equal to) Below
Dashed Line
Dashed Line
Solid Line
Solid Line
GRAPHING LINEAR INEQUALITIES
Less than Less than and/or equal to
Greater thanGreater than and/or equal to
Inequality
STEPS TO GRAPHING INEQUALITIES
Remember: ≤ and ≥ will use a solid line
< and > will use a dashed line
Change the inequality sign to an equal sign; then graph the equation
Step 1:Change the
inequality sign, Graph the line
STEPS IN GRAPHING INEQUALITIES
Remember: If greater than, greater than and/or equal
to, shade above the inequality
If less than, less than and/or equal to, shade below the inequality
Can use a test point to check if the shaded part of the graph contains the inequality solutions.
Step 2: Determine which half of the graph should be shaded
STEPS TO GRAPHING INEQUALITIES
Shade the part of the graph that contains the solutions.
Step 3: Shade
EXAMPLE 1
Step 1: Change the
sign, and graph the line
Step 2: Determine which half of the graph should be shaded
Step 3: Shade
Use a graph to solve y≤ 2x + 3
EXAMPLE 1
Use a graph to solve y ≤ 2x + 3
y ≤
2x
+3
30
300
3)0(20
32
)0,0(
32
32
xy
xy
xyChange the sign
Test Point
Test the point in original inequalityTrue
EXAMPLE 2
Use a graph to solve y > -x + 4
EXAMPLE 2
40
4)0(0
4
)0,0(
4
4
xy
xy
xyChange sign
Test Point
Test the point in original inequalityFalse
y > -x +
4 Use a graph to solve y > -x + 4
PRACTICE PROBLEMS
Use a graph to solve the following inequalities
1. y < x -72. y ≥ -3x - 33. y> x4. y ≤ 2x - 4
WHAT DID WE LEARN TODAY?1. What kind of line is less than or greater
than?2. What kind of line is greater than or equal to
and less than or equal to?3. If the inequality is greater than, greater
than or equal to, what part of the graph is shade?
4. If the inequality is less than, less than or equal to, what part of the graph is shade?
5. What are the three steps to graphing linear inequalities?