Calculate Rate of Change from a Graph
This calculator helps you find the rate of change (slope) between two points on a graph.
The rate of change will be displayed here.
Understanding Rate of Change from a Graph
The rate of change, often referred to as the slope in the context of a graph, quantifies how one variable (the dependent variable, typically plotted on the y-axis) changes with respect to another variable (the independent variable, typically plotted on the x-axis). In simpler terms, it tells you how steep a line is and in which direction it is going.
The Formula
The formula for calculating the rate of change (slope, denoted by 'm') between two points (x1, y1) and (x2, y2) on a graph is:
m = (y2 - y1) / (x2 - x1)
This formula represents the "rise" (change in y) over the "run" (change in x).
Interpreting the Rate of Change
- Positive Rate of Change: The line slopes upwards from left to right, indicating that as the x-value increases, the y-value also increases.
- Negative Rate of Change: The line slopes downwards from left to right, indicating that as the x-value increases, the y-value decreases.
- Zero Rate of Change: The line is horizontal, meaning the y-value remains constant regardless of the x-value.
- Undefined Rate of Change: The line is vertical, meaning the x-value remains constant while the y-value changes. This occurs when x2 = x1, leading to division by zero.
Example Calculation
Let's say we have two points on a graph: Point A at (2, 5) and Point B at (6, 13).
- x1 = 2
- y1 = 5
- x2 = 6
- y2 = 13
Using the formula:
m = (13 - 5) / (6 - 2)
m = 8 / 4
m = 2
In this example, the rate of change is 2. This means for every 1-unit increase in the x-value, the y-value increases by 2 units.