What does the dashed line in the graph of an inequality represent?

The dashed line represents the boundary of the solution set, but the points on the line are not included in the solution.

Explain how you would determine whether to shade above or below the line when graphing y > mx + b.

Since the inequality is 'y is greater than', you would shade above the line because all the y-values greater than the line are solutions to the inequality.

Is the point (0, 0) a solution to the inequality y < 4x + 3? Explain your reasoning.

Yes, (0, 0) is a solution because when you substitute x=0 and y=0 into the inequality, you get 0 < 4(0) + 3, which simplifies to 0 < 3. This is a true statement.

Write an inequality that would be represented by a dashed line with the area below the line shaded.

y < mx + b, where m and b are any real numbers.

Graphing Inequalities Lesson Plan for Grade 8th Grade

Lesson Preview

Learning Objective

I can graph two-variable inequalities on a coordinate plane and identify the solution set.

1
To graph the inequality y ≤ 4x + 3, first graph the line y = 4x + 3, noting the y-intercept is 3 and the slope is 4, then shade the area below the line.
2
When graphing y > –x/2 – 6, graph the line y = –x/2 – 6 as a dashed line to show that the line itself is not included in the solution.
3
The solution set of an inequality includes all the points on the coordinate plane that satisfy the inequality, which can be a region above or below a line.

Graphing Inequalities

Lesson Preview

Learning Objective

Warm-Up Video

Key Concepts

Practice Questions

Exit Ticket

Related Lessons

Lines of Symmetry in Shapes

Using Order of Operations

Multiplying Powers with the Same Base

Related Lessons

Lines of Symmetry in Shapes

Using Order of Operations

Multiplying Powers with the Same Base

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