Math Problem Statement

Graph the inequality in the coordinate plane. y ≥ -3

Solution

The inequality you need to graph is:

y3y \geq -3

This inequality represents all points on the coordinate plane where the value of yy is greater than or equal to 3-3.

Steps to graph this:

  1. Draw the boundary line: The boundary for this inequality is the horizontal line y=3y = -3. Since the inequality includes \geq (greater than or equal to), the line will be solid to indicate that points on the line are included in the solution.

  2. Shade the solution region: The inequality specifies y3y \geq -3, meaning the solution is all the points where yy is greater than or equal to 3-3. Thus, you'll shade the area above the line, including the line itself.

Graph description:

  • The line is horizontal and runs parallel to the x-axis at y=3y = -3.
  • The shaded region will be above this line, including the line itself.

Would you like me to generate a visualization of this graph?

Related questions:

  1. How would the graph change if the inequality was y>3y > -3?
  2. What happens if the inequality is y3y \leq -3?
  3. How do you determine whether to use a solid or dashed line in an inequality graph?
  4. How can you test if a point satisfies the inequality y3y \geq -3?
  5. What would be the solution if the inequality was x3x \geq -3?

Tip:

Always pay attention to the direction of the inequality symbol to know whether to shade above or below the line.

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Math Problem Analysis

Mathematical Concepts

Inequalities
Coordinate Geometry

Formulas

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Theorems

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Suitable Grade Level

Grades 7-10