Match each equation with the sketch that most closely resembles its graph. x = 5

Verified step by step guidance

1. Recognize that the equation \(x = 5\) represents a vertical line in the coordinate plane because it states that the x-coordinate is always 5 regardless of the y-coordinate.
2. Recall that vertical lines have the form \(x = a\), where \(a\) is a constant, and they run parallel to the y-axis.
3. Understand that the graph of \(x = 5\) will be a straight line crossing the x-axis at the point (5, 0).
4. Note that this line does not slope or curve; it extends infinitely up and down through all y-values while maintaining \(x = 5\).
5. When matching the equation to a sketch, look for the graph that shows a vertical line passing through \(x = 5\) on the x-axis.

Key Concepts

Vertical Lines

A vertical line is a line where all points have the same x-coordinate. Its equation is of the form x = a constant, such as x = 5. This line runs parallel to the y-axis and does not depend on y-values.

Graphing Linear Equations

Graphing linear equations involves plotting all points (x, y) that satisfy the equation. For equations like x = 5, the graph is a straight line where x is fixed, illustrating the concept of lines with undefined slope.

Coordinate Plane and Axes

The coordinate plane consists of the x-axis (horizontal) and y-axis (vertical). Understanding the position of lines relative to these axes helps in matching equations to their graphs, such as recognizing that x = 5 is a vertical line crossing the x-axis at 5.