Math Problem Statement

Which graph below represents the inequality y ≤ 3?

Solution

The inequality y3y \leq 3 represents the region on the coordinate plane where the yy-coordinate of points is less than or equal to 3. This means the boundary line is y=3y = 3, 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 y=3y = 3, with shading below the line and the line itself being solid. This correctly represents the inequality y3y \leq 3.
  • 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:

  1. How do you graph y3y \geq 3 on a coordinate plane?
  2. What is the difference between a solid and a dashed line in inequalities?
  3. How do you represent the inequality y<3y < 3 on a graph?
  4. Can inequalities be represented in three-dimensional space?
  5. How do you solve a system of inequalities graphically?

Tip: A solid line in an inequality graph (like y3y \leq 3) means that the boundary is included in the solution set, while a dashed line means it is not.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Graphing Inequalities
Coordinate Plane

Formulas

-

Theorems

Boundary Line Theorem for Inequalities

Suitable Grade Level

Grades 6-8