Find the Slope of a Line - Algebra-2

1. Fundamental Concepts

Slope Definition: The slope of a non-vertical line is the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.
Formula: For two points and on a line, the slope m is calculated as ，where represents the vertical change (rise) and represents the horizontal change (run).

Slope Significance:
- A positive slope () means the line rises from left to right.
- A negative slope () means the line falls from left to right.
- A zero slope () indicates a horizontal line (no vertical change).
- An undefined slope occurs for a vertical line (no horizontal change, as the denominator in the slope formula becomes 0).

Step 1: Identify the coordinates of the two points, labeling them as and (order does not affect the result).
Step 2: Calculate the vertical change by finding the difference in the y-coordinates: .
Step 3: Calculate the horizontal change by finding the difference in the x-coordinates: .
Step 4: Divide the vertical change by the horizontal change to get the slope, using the formula .
Step 5: Determine the nature of the slope (positive, negative, zero, or undefined) based on the result.