Finding the slope of a line is a fundamental concept in algebra and geometry. The slope measures the steepness or incline of a line. It’s calculated as the ratio of the change in the vertical direction (y-coordinates) to the change in the horizontal direction (x-coordinates) between two points on the line.

Here’s how to find the slope:

**Step 1: Select Two Points on the Line**

- Choose any two points on the line. Label these points as (x₁, y₁) and (x₂, y₂).

**Step 2: Calculate the Change in Y (Δy)**

- Subtract the y-coordinate of the first point from the y-coordinate of the second point: Δ�=�2−�1Δ
*y*=*y*2−*y*1

**Step 3: Calculate the Change in X (Δx)**

- Subtract the x-coordinate of the first point from the x-coordinate of the second point: Δ�=�2−�1Δ
*x*=*x*2−*x*1

**Step 4: Find the Slope (m)**

- Divide the change in y by the change in x: �=Δ�Δ�
*m*=Δ*x*Δ*y*

This gives you the slope of the line.

**Example**:

Suppose you have two points on a line: �(2,3)*A*(2,3) and �(5,9)*B*(5,9).

**Calculate Δy**: Δ�=�2−�1=9−3=6Δ*y*=*y*2−*y*1=9−3=6**Calculate Δx**: Δ�=�2−�1=5−2=3Δ*x*=*x*2−*x*1=5−2=3**Find the Slope (m)**: �=Δ�Δ�=63=2*m*=Δ*x*Δ*y*=36=2

So, the slope of the line passing through points A and B is �=2*m*=2.

**Additional Information**:

- A positive slope (m > 0) indicates a line that rises as you move from left to right.
- A negative slope (m < 0) indicates a line that falls as you move from left to right.
- A slope of zero (m = 0) indicates a horizontal line.
- A line with an undefined slope is vertical.

Understanding slope is crucial in various mathematical and real-world applications, including graphing, engineering, physics, and economics.