Graph the line passing through the given point and having the indicated slope. Plot twopoints on the line. See Example 7. through (9/4 , 2), undefined slope

Verified step by step guidance

1. Understand that an undefined slope indicates a vertical line.
2. A vertical line through a point (x_0, y_0) has the equation x = x_0.
3. Since the line passes through the point (9/4, 2), the equation of the line is x = 9/4.
4. To plot the line, choose any two points with x-coordinate 9/4, such as (9/4, 0) and (9/4, 3).
5. Draw a vertical line through these points to represent the line with an undefined slope.

Key Concepts

Slope

The slope of a line measures its steepness and direction, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. An undefined slope occurs when a line is vertical, meaning it has no horizontal change, resulting in a division by zero. This indicates that all points on the line share the same x-coordinate.

Graphing a Line

Graphing a line involves plotting points on a coordinate plane based on their x and y values. For a line with an undefined slope, you only need to plot the given point and draw a vertical line through it. This line will extend infinitely in both the upward and downward directions, representing all points with the same x-coordinate.

Coordinate System

A coordinate system is a two-dimensional plane 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), where 'x' indicates the position along the x-axis and 'y' indicates the position along the y-axis. Understanding this system is crucial for accurately plotting points and lines.