Graphing Inequalities on a Coordinate Plane

The rectangular coordinate system is a powerful tool for algebraic calculations and real-world applications. By understanding how to graph linear inequalities on a coordinate plane, we can solve problems that involve two variables. In this article, we will explore the basics of graphing inequalities and examine some real-world scenarios.

A rectangular coordinate system consists of two intersecting number lines, one horizontal and one vertical. The horizontal line is called the x-axis, while the vertical line is called the y-axis. These axes divide a plane into four regions, known as quadrants. Quadrant I is located in the top-right corner, while quadrant II is located in the top-left corner. Quadrant III is located in the bottom-left corner, and quadrant IV is located in the bottom-right corner.

To graph an inequality on a coordinate plane, we need to first identify the coordinates of the points that satisfy the inequality. For example, let's consider the inequality y = 5/2. Since y = 5/2 is equal to 2.5, the point is above the x-axis. Similarly, if we have an inequality like x = 3, the point is located to the right of the y-axis.

By plotting these points on a coordinate plane and connecting them with a line, we can create the graph of a linear inequality. For instance, let's consider the point (2, -3) on the coordinate plane. Since y = -3, the point is below the x-axis. Also, since x = 2, the point is located to the right of the y-axis. This means that the point (2, -3) lies in quadrant IV.

The rectangular coordinate system has many real-world applications. For instance, when filling up a gas tank with gasoline, we need to consider how much it will cost based on the number of gallons and the price per gallon. By graphing the inequality for this problem, we can determine exactly how much it would cost to fill up our car.

In conclusion, graphing inequalities on a coordinate plane is an essential skill in algebra that has many real-world applications. By understanding how to plot points and create graphs, we can solve problems that involve two variables and make informed decisions in everyday life.

* The rectangular coordinate system consists of two intersecting number lines, one horizontal and one vertical.

* Quadrants are identified by Roman numerals, starting from the upper-right corner and proceeding counterclockwise.

* To graph an inequality on a coordinate plane, we need to identify the coordinates of the points that satisfy the inequality and plot them on the plane.

Real-World Application

* Filling up a gas tank with gasoline: By graphing the inequality for this problem, we can determine exactly how much it would cost to fill up our car.

Graphing inequalities on a coordinate plane