## All You Need To Know About Rate Of Change Calculations

The rate of change formula or calculator is used to calculate the slope between two points plotted on a line. It thus denotes the slope of the line and is basically the ratio between the difference in the x and y co-ordinates.

For example, if point A is denoted by (x

_{1}, y_{1}) and point B is denoted by (x_{2}, y_{2}) where the two points are present on a line L, the rate of change or the slope of the line L = (y_{2 – }y_{1})/ (x_{2}– x_{1})

Thus, for two points say (5, 3) and (19, 15), the rate of change calculator is the ratio of (19-5)/(15-3)= 12/12 = 1.

This is quite an important concept in a variety of sciences. The rate of change finds application in the following areas:

- Distance and Speed Problems
- Statistics and Population
- Calculating Growth
- Calculus

There are many more applications of the rate of change concept; for the purpose of illustration, let us consider the distance and speed related problems. Velocity is described as the rate at which a particular distance is covered in a specific time frame. Acceleration is the rate of change of velocity with respect to time. Similarly, there are a plethora of applications for this concept.

Let us understand a simple application of rate of change with an example.

### Example

**Problem Statement:**

If Timmy has 10 gallons of gas in his bike and has 6 left after driving 200 miles, what does the rate of slope indicate and what is the bike’s mileage?

**Solution:**

Difference in Gas Quantity = Consumption of gas for the trip = Initial Quantity – Final Quantity = 10-6 = 4 gallons

Distance Traveled = 200 miles

When we plot the distance on the X axis and the quantity of gas on the Y axis, the initial point at the starting would be at 0 miles and 10 gallons i.e. (0,10) in the co-ordinates while the final c0-ordinates when he reaches his destination would be 200 miles and 6 gallons = (200,6).

Rate of Change = (6-10)/ (200-0) = -4/200 = -1/50 = -.02

Coming to the implication of this slope, it simply means that Timmy’s bike is using up .02 gallons of gas for every mile it is being used. The –ve sign indicates a decrease.

The above inference is simple – the rate of change here = Difference in fuel / Distance

(Gallons/mil e) = Fuel used per mile.

However, the number of miles per gallon is a more useful measure in this case and this can be written down by seeing the slope as 50 miles (from the denominator) per gallon (from the numerator).

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