In Exercises 49–58, graph each equation in a rectangular coordinate system. 3x -18=0

Verified step by step guidance

1. Identify the type of equation: The given equation is a linear equation in one variable, which can be rewritten as \(3x - 18 = 0\).
2. Solve for \(x\): Add 18 to both sides of the equation to isolate the term with \(x\), resulting in \(3x = 18\).
3. Divide both sides by 3 to solve for \(x\): \(x = \frac{18}{3}\).
4. Recognize the graph type: Since the equation simplifies to \(x = 6\), this represents a vertical line in the coordinate plane.
5. Plot the graph: Draw a vertical line that passes through \(x = 6\) on the x-axis. This line is parallel to the y-axis.

Key Concepts

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. The general form is Ax + B = 0, where A and B are constants. In the given equation, 3x - 18 = 0, it can be rearranged to find the value of x, which represents a straight line when graphed.

Graphing Linear Equations

Graphing a linear equation involves plotting points that satisfy the equation on a coordinate plane. For the equation 3x - 18 = 0, solving for x gives x = 6, indicating a vertical line at x = 6. Understanding how to represent this visually is crucial for interpreting the relationship between variables.

Rectangular Coordinate System

A rectangular coordinate system, also known as the Cartesian coordinate system, consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Each point in this system is defined by an ordered pair (x, y). This framework is essential for graphing equations and understanding their geometric interpretations.