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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?

What graphs require shading? Shading above the line? Below the line?

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

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.

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.

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