Calculating the Slope of a Graph:

To calculate the slope of a graph, we need to determine how the dependent variable (y-axis) changes with respect to the independent variable (x-axis). The slope measures the steepness or incline of the graph at any given point. It can be calculated using the formula:

Slope (m) = Change in y / Change in x

To apply this formula, we follow a step-by-step process:

Step 1: Identify two points on the graph
Choose two points on the graph. These points should have known x and y coordinates. It is generally easier to select points that lie on a straight line portion of the graph.

Step 2: Determine the coordinates of the two points
Identify the x and y coordinates for both points. Let's denote the coordinates of the first point as (x1, y1) and the second point as (x2, y2).

Step 3: Calculate the change in y
Subtract the y-coordinate of the first point from the y-coordinate of the second point:
Change in y = y2 - y1

Step 4: Calculate the change in x
Subtract the x-coordinate of the first point from the x-coordinate of the second point:
Change in x = x2 - x1

Step 5: Calculate the slope
Divide the change in y by the change in x to find the slope:
Slope (m) = Change in y / Change in x

Step 6: Interpret the slope
The resulting value of the slope represents the rate at which the dependent variable changes with respect to the independent variable. A positive slope indicates an upward trend, while a negative slope indicates a downward trend. The magnitude of the slope determines the steepness of the graph.

Example:
Let's say we have two points on a graph: (2, 5) and (4, 9).
Using the formula:
Change in y = 9 - 5 = 4
Change in x = 4 - 2 = 2
Slope (m) = 4 / 2 = 2

Interpretation:
The slope of the graph is 2, indicating that for every one unit increase in the x-coordinate, there is a corresponding increase of 2 units in the y-coordinate.

Note:
- If the graph is a straight line, the slope remains constant throughout.
- If the graph is curved, the slope will vary at different points.
- The slope can also be calculated using other methods, such as using the tangent of the angle between the line and the x-axis.