# Rate of Change Calculator

**Rate of Change Calculator** is an online tool that helps to calculate the rate at which one quantity is changing with respect to another quantity. The slope of a straight line is used to represent the rate of change graphically.

## What is the Rate of Change Calculator?

Rate of Change Calculator helps to compute the rate of change of one quantity with respect to another when we know the input coordinate points. The rate of change is used to observe how an output quantity changes relative to an input quantity. To use the rate of change calculator, enter the values in the input boxes.

### Rate of Change Calculator

## How to Use the Rate of Change Calculator?

Please follow the steps below to find the rate of change using the rate of change calculator

**Step 1:**Go to Cuemath's online rate of change calculator.**Step 2:**Enter the values in the given input boxes.**Step 3:**Click on the**"Calculate"**button to find the rate of change.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values.

## How Does Rate of Change Calculator Work?

The rate of change is expressed in the form of a ratio between the change in one variable and a corresponding change in the other variable. Another way of describing the rate of change is by using a linear function. Thus, we can also say that the rate of change is represented by the slope of a line. Suppose the equation of a straight line is given by y = mx + c. Here, 'm' is known as the slope and it represents the rate of change. The rate of change is given by the following formulas:

Rate of change = change in y / change in x

\(\frac{\Delta y}{\Delta x} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

The rate of change can be both positive or negative.

- When the value of x increases and there is a corresponding increase in the value of y then the rate of change is positive. Such a graph slants upwards.
- When the value of x increases and there is a corresponding decrease in the value of y then the rate of change is negative. Such a graph slants downwards.
- A zero rate of change implies that a quantity does not change over time. Thus, as the value of x increases the value of y remains constant. Such a graph is a horizontal line.

## Solved Examples on Rate of Change Calculator

**Example 1:**

Find the rate of change if the coordinates are (5, 2) and (7, 8). Verify the result using the online rate of change calculator

**Solution:**

Rate of change or slope = change in y/change in x

= (y_{2 }- y_{1}) / (x_{2} - x_{1})

= (8 - 2) / (7 - 5)

= 6 / 2

= 3

The rate of change is positive. Thus, the graph will slant upwards.

**Example 2:**

Find the rate of change if the coordinates are (32.5, 15) and (30, 25.7). Verify the result using the online rate of change calculator

**Solution:**

Rate of change or slope = change in y/change in x

= (y_{2 }- y_{1}) / (x_{2} - x_{1})

= (25.7 - 15) / (30 - 32.5)

= 10.7/ (-2.5)

= -4.28

The rate of change is negative. Thus, the graph will slant downwards.

Similarly, you can try the rate of change calculator to find the rate of change for the following:

- (-5.3, 2) and (2.1, 7)
- (8.9, -4.5) and (10.7, 12)

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