Graph each equation in a rectangular coordinate system. 3x -18=0

Verified step by step guidance

1. Identify the given equation: \$3x - 18 = 0$.
2. Rewrite the equation to isolate \(x\): add 18 to both sides to get \$3x = 18$.
3. Divide both sides by 3 to solve for \(x\): \(x = \frac{18}{3}\).
4. Simplify the right side to find the constant value of \(x\): \(x = 6\).
5. Interpret the equation \(x = 6\) as a vertical line crossing the x-axis at 6; to graph it, draw a straight vertical line through all points where \(x\) is 6.

Key Concepts

Linear Equations in Two Variables

A linear equation in two variables, such as x and y, represents a straight line when graphed on the coordinate plane. The equation 3x - 18 = 0 can be rewritten to isolate one variable, helping to identify the line's position.

Graphing Vertical and Horizontal Lines

Equations like 3x - 18 = 0 simplify to x = 6, which represents a vertical line crossing the x-axis at 6. Vertical lines have undefined slope and all points on the line share the same x-coordinate.

Coordinate Plane and Plotting Points

The rectangular coordinate system consists of the x-axis and y-axis intersecting at the origin. To graph an equation, plot points that satisfy the equation and connect them, which for vertical lines means plotting points with the same x-value and varying y-values.