Math Problem Statement
Which graph below represents the inequality y ≤ 3?
Solution
The inequality represents the region on the coordinate plane where the -coordinate of points is less than or equal to 3. This means the boundary line is , and the region below this line (including the line itself) should be shaded.
Looking at the graphs provided in the image:
- Graph A shows a horizontal boundary at , with shading below the line and the line itself being solid. This correctly represents the inequality .
- The other graphs (B, C, and D) either have shading above the line or use a dashed line, which does not match the inequality.
Therefore, the correct answer is a. A.
Would you like further details on graphing inequalities or any related questions? Here are some follow-up questions:
- How do you graph on a coordinate plane?
- What is the difference between a solid and a dashed line in inequalities?
- How do you represent the inequality on a graph?
- Can inequalities be represented in three-dimensional space?
- How do you solve a system of inequalities graphically?
Tip: A solid line in an inequality graph (like ) means that the boundary is included in the solution set, while a dashed line means it is not.
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Math Problem Analysis
Mathematical Concepts
Graphing Inequalities
Coordinate Plane
Formulas
-
Theorems
Boundary Line Theorem for Inequalities
Suitable Grade Level
Grades 6-8