key term - Quadrant

Definition

A quadrant is one of the four equal parts into which a plane or a sphere is divided by two intersecting lines or planes that are perpendicular to each other. It is a fundamental concept in the context of graphing linear inequalities in two variables.

5 Must Know Facts For Your Next Test

1. The four quadrants in a coordinate plane are labeled I, II, III, and IV, and are defined by the positive and negative signs of the x and y coordinates.
2. The sign of the x and y coordinates determines the location of a point in a specific quadrant, which is crucial for understanding the behavior of linear inequalities.
3. Graphing linear inequalities in two variables involves shading the appropriate region of the coordinate plane based on the given inequality.
4. The orientation of the inequality (greater than, less than, etc.) and the signs of the coefficients determine which quadrant(s) will be shaded.
5. Analyzing the quadrants where the solution set of a linear inequality lies can provide valuable insights into the relationship between the variables.

Review Questions

• Explain how the four quadrants of the coordinate plane are defined and how the signs of the x and y coordinates determine the location of a point in a specific quadrant.
  • The four quadrants of the coordinate plane are defined by the positive and negative signs of the x and y coordinates. Quadrant I has positive x and y coordinates, Quadrant II has negative x and positive y coordinates, Quadrant III has negative x and y coordinates, and Quadrant IV has positive x and negative y coordinates. The sign of the x and y coordinates determines the location of a point in a specific quadrant, which is crucial for understanding the behavior of linear inequalities.
• Describe how the orientation of a linear inequality and the signs of its coefficients affect the shading of the solution set on the coordinate plane.
  • When graphing a linear inequality in two variables, the orientation of the inequality (greater than, less than, etc.) and the signs of the coefficients determine which quadrant(s) will be shaded. For example, a linear inequality with a positive slope and a greater than or equal to sign will result in the shading of the half-plane above the line, which may include one, two, or three quadrants depending on the specific coefficients. Understanding the relationship between the quadrants and the solution set is essential for accurately graphing and interpreting linear inequalities.
• Analyze how the quadrants where the solution set of a linear inequality lies can provide insights into the relationship between the variables.
  • $$The quadrants where the solution set of a linear inequality lies can reveal important information about the relationship between the variables. For example, if the solution set is located in Quadrants I and II, it suggests that as one variable increases, the other variable decreases. Conversely, if the solution set is in Quadrants I and IV, it indicates that as one variable increases, the other variable also increases. By analyzing the quadrants involved, you can gain valuable insights into the nature of the relationship between the variables in the linear inequality.$$

Related terms

Coordinate Plane:

A two-dimensional plane that uses an x-axis and a y-axis to locate points and represent relationships between quantities.

Axis Intercepts: The points where a graph intersects the x-axis and y-axis, providing important information about the behavior of the function.

Slope:

The measure of the steepness of a line, indicating the rate of change between the x and y variables.