91Ó°ÊÓ

Coordinate geometry, also known as analytic geometry, involves studying geometry by plotting points, lines, and curves on a coordinate plane. Each point is represented by a pair of values called coordinates. These coordinates are typically labeled as

• the x-coordinate, representing the horizontal position, and
• the y-coordinate, representing the vertical position.

In our exercise, we worked with the coordinates

• \((-3, -6)\).

Understanding how to plot and interpret these coordinates on a grid is fundamental in coordinate geometry. In this context, each point on the plane can represent a solution or potential solution to geometric problems or equations.
For linear inequalities, plotting the right coordinates helps you visualize which areas of the plane satisfy the inequality.

Linear inequalities are expressions where one side of the equation is not necessarily equal to the other. Instead, it could be greater than, less than, greater than or equal to, or less than or equal to it. An example is \[ y > 3x + 2 \].
Such inequalities represent a region in the coordinate plane rather than a single line. For example, in the inequality \( y > 3x + 2 \), the expression \( 3x + 2 \) describes a line, and the inequality \( y > 3x + 2 \) means every point above this line makes the inequality true.

• The boundary line can be plotted by converting the inequality to an equation, like \( y = 3x + 2 \),and plotting it on the graph.
• To determine which side of the line the inequality represents, choose a test point not on the line. Substitute its coordinates into the inequality to check if it satisfies the condition.

This visual method helps students understand what solutions qualify under the inequality logically.

An algebraic expression is a combination of numbers, variables, and arithmetic operations without an equality or inequality sign. They form the foundation of solving more complex math problems, like inequalities and equations. In our problem, \( 3x + 2 \) is an algebraic expression that forms the right-hand side of the inequality.

• The number \(3\) is the coefficient of \(x\), indicating how much \(x\) will be multiplied by in the expression.
• The \(+2\) is a constant term, which adjusts the entire expression upward or downward on the graph.

Understanding what each part of the expression represents is crucial. By substituting values for \(x\), you can generate corresponding values for \(y\), which are used to plot or examine inequalities involving variables.
Manipulating algebraic expressions, like we do in inequalities, helps develop strong algebraic skills necessary for solving real-world problems.