# Lesson 5.6 - PowerPoint PPT Presentation

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Lesson 5.6. Graphing Inequalities in Two Variables. Each group member should choose a different statement from the list below. y □ 1+0.5x y □ -1-2x y □ 1-0.5x y □ 1-2x.

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Lesson 5.6

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### Lesson 5.6

Graphing Inequalities in Two Variables

Each group member should choose a different statement from the list below.

• y □ 1+0.5x

• y □ -1-2x

• y □ 1-0.5x

• y □ 1-2x

Evaluate the right side of the statement for x = -3. For each circle in the first column on the graph, fill in > if the y-value is greater than your value, = if the values are equal, and < if the y-value is less than your value.

Evaluate the right side of the statement for x = -2. For each circle in the first column on the graph, fill in > if the y-value is greater than your value, = if the values are equal, and < if the y-value is less than your value.

Repeat the last step for x = -1, 0, 1, 2, and 3.

### Analyze the Results

What do you notice about the circles filled with the equal sign? Describe any other patterns you see.

Test a point with fractional or decimal coordinates that is not represented by a circle on the grid. Compare your results with the symbols on the same side of the line of equal signs as your point.

### Analyze the Results

Next to the xy axis, at the bottom of the template, write your statement with the “less than” symbol, <. Shade the region of points that makes your statement true. If the points on the line make an inequality true, draw a solid line through them.

Repeat the last step with >, ≤, ≥, and =.

### Analyze the Results

Compare your graphs with those of others in your group. What graphs require a solid line? A dashed line?

Discuss how to use one point to check the graph of an inequality.

### Example

• Graph the inequality 2x – 3y > 3.

2x – 3y > 3

– 3y > 3- 2x

y < -1+ (2/3)x

### Example

• Check to see whether each point is part of the solution.

y < -1+ (2/3)x

(3,-2)

(3,1)

(-1,2)

(-2,-3)

### Testing an Inequality on the Graphing Calculator

• On the home screen type the inequality statement 2x-3y>3 with the x and y from one of the coordinates substituted into the inequality:

• 2(3)-3(-2)>3

• Press Enter.

• If the statement is true a 1 will be printed. If the statement is false, a 0 will be printed.

• Try the other points.

### Graphing Inequalities

• Draw a broken or dashed line on the boundary for inequalities with > or <.

• Draw a solid line on the boundary for inequalities with ≥ or ≤.

• To graph inequalities in the form y< or y≤ shade below the boundary line.

• To graph inequalities in the form y> or y≥ shade above the boundary line.

3y<1

y<1/3

x> 2

3-y<7

-y<4

y>-4

-2x≥5

X≤-2.5

### In this Section

• You solved two-variable inequalities for y

• You graphed inequalities on the coordinate plane and showed the solutions as the half planes.