Rate of Decrease Calculator
Enter the coordinates of two points from your graph to calculate the rate of change.
e.g., Time, Distance, Year
e.g., Value, Temperature, Speed
e.g., Later Time, Further Distance
e.g., Lower Value, Lower Temp
Calculation Results
Change in X (Δx):
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Change in Y (Δy):
–
Slope (Rate of Change):
–
Rate of Decrease:
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How to Calculate Rate of Decrease from a Graph
Calculating the rate of decrease from a graph is an essential skill in physics, economics, and mathematics. It allows you to quantify how quickly a value is dropping over a specific interval. In mathematical terms, this is equivalent to finding the slope of the line connecting two points, where a negative slope indicates a decrease.
The Formula
The rate of decrease is derived from the slope formula ($m$). The slope represents the "rise over run," or the change in the vertical axis ($y$) divided by the change in the horizontal axis ($x$).
Rate = Δy / Δx = (y₂ – y₁) / (x₂ – x₁)
Where:
- x₁, y₁ are the coordinates of the starting point.
- x₂, y₂ are the coordinates of the ending point.
Step-by-Step Guide
- Identify Two Points: Select two distinct points on the line graph where the line is going downwards (from left to right). Let's call them Point A and Point B.
- Find Coordinates: Determine the $x$ and $y$ values for both points. For example, Point A might be $(0, 100)$ and Point B might be $(5, 60)$.
- Calculate the Vertical Change (Δy): Subtract the first y-value from the second y-value ($60 – 100 = -40$).
- Calculate the Horizontal Change (Δx): Subtract the first x-value from the second x-value ($5 – 0 = 5$).
- Divide: Divide the vertical change by the horizontal change ($-40 / 5 = -8$).
In this example, the slope is -8. This means the Rate of Decrease is 8 units per unit of x.
Understanding the Results
When analyzing graphs:
- Negative Slope: Indicates a decrease. The steeper the line falls, the higher the rate of decrease.
- Zero Slope: Indicates no change (a horizontal line).
- Positive Slope: Indicates an increase (not a decrease).
Real-World Example
Imagine a car depreciating in value.
Year 0 (x₁): Value is 20,000 (y₁)
Year 4 (x₂): Value is 12,000 (y₂)
Calculation: (12,000 – 20,000) / (4 – 0) = -8,000 / 4 = -2,000.
The car's rate of decrease in value is 2,000 per year.