Graph the line passing through the given point and having the indicated slope. Plot two points on the line. See Example 7. through (- 5/2 , 3), undefined slope

Verified step by step guidance

1. Step 1: Understand the problem. We are asked to graph a line that passes through the point (-5/2, 3) and has an undefined slope. An undefined slope means that the line is vertical.
2. Step 2: Plot the given point on the graph. The point (-5/2, 3) is located at -2.5 on the x-axis and 3 on the y-axis.
3. Step 3: Draw a vertical line through the point (-5/2, 3). This line represents the line with an undefined slope.
4. Step 4: Choose two points on the line. Since the line is vertical, the x-coordinate for any point on the line will be -5/2 or -2.5. You can choose any two points on the line, for example (-5/2, 0) and (-5/2, 5).
5. Step 5: Plot these two points on the graph and make sure they lie on the line you drew in step 3. This confirms that the line you drew is correct.

Key Concepts

Slope

Slope is a measure of the steepness or incline of a line, 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 there is no horizontal change, and thus the slope cannot be defined as a number. In this case, the line will pass through the given point and extend vertically.

Graphing a Line

Graphing a line involves plotting points on a coordinate plane based on a specific equation or slope. For a line with an undefined slope, you will plot the given point and draw a vertical line through it. This line will not have any horizontal movement, indicating that all points on the line share the same x-coordinate as the given point.

Coordinate Plane

A coordinate plane is a two-dimensional surface defined by a horizontal axis (x-axis) and a vertical axis (y-axis). Each point on the plane is represented by an ordered pair (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position. Understanding how to navigate this plane is essential for accurately plotting points and lines.