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.
2. Understand that a vertical line is a line where all points have the same x-coordinate, in this case, 5.
3. Visualize the graph: it is a straight line parallel to the y-axis, crossing the x-axis at \( x = 5 \).
4. Note that this line does not depend on the y-coordinate, meaning it extends infinitely in both the positive and negative y-directions.
5. Match this description with the graph that shows a vertical line intersecting the x-axis at \( x = 5 \).

Key Concepts

Vertical Lines

The equation x = 5 represents a vertical line in the Cartesian coordinate system. This line is drawn parallel to the y-axis and intersects the x-axis at the point (5, 0). Vertical lines have an undefined slope and indicate that for any value of y, the x-coordinate remains constant at 5.

Graphing Linear Equations

Graphing linear equations involves plotting points that satisfy the equation and connecting them to form a straight line. In the case of x = 5, every point on the line has the same x-coordinate, which simplifies the graphing process to drawing a straight line at x = 5 across all values of y.

Coordinate Plane

The coordinate plane is a two-dimensional surface defined by a horizontal axis (x-axis) and a vertical axis (y-axis). Each point on this plane is represented by an ordered pair (x, y). Understanding the layout of the coordinate plane is essential for accurately interpreting and sketching graphs of equations.