How do you find the rate of change?

Frays of change is how much x. Ganges w time or another variable . So this can be done by working out the gradient of a graph or differentiating If it is an expression

Linear functions have a constant rate of change which is represented as the gradient of the graph.

It is simply the change of y-values with respect to x-values i.e. (y1-y2) / (x1-x2) where (x1,y1), (x2,y2) are the coordinates

the change in y-values by the change in x-values.

The rate of change measures how one quantity changes relative to another. In mathematics, it is often calculated using derivatives in calculus or the difference between two points in algebra. Here are the common methods to find the rate of change:

1. Average Rate of Change (Algebraic Approach)

The average rate of change between two points on a function is calculated as the slope of the line connecting the points. This is given by:

2. Instantaneous Rate of Change (Using Derivatives)

The instantaneous rate of change of a function at a specific point is the value of the derivative at that point.

This gives the slope of the tangent line to the curve at x=ax = ax=a, representing how the function changes at that exact point.

The Rate of change (ROC) is the increase or decrease of one value related to another value.

The speed of a car for instance is the distance covered divided by the time taken.

In mathematics this can be the gradient of a graph in general terms.

It is simply a total concerned amount divided by the total time. For example, if you want to find out rate of change of distance. You consider total distance covered by the vehicle and divide it by the total time it took for that change.

Rate of change of position = total covered distance / total taken time.

find the change in y over change in x using triangle on give graph

To find the average rate of change of a function over an interval, you can use the formula:

Average Rate of Change = (Change in Y) / (Change in X) = (ΔY) / (ΔX)

You would have to differentiate

The rate of change (ROC) is how much the value of something changes over a period of time and it is given in percentage terms.

To find this you first calculate the change in "Y" values (or the change in an outcome variable) divided by the change in "X" values (or the change in input variables).

So if my tutoring time increases from 3 hours in week 1 to 16 hours in week 2 and my income increases from £45 per week to £240 per week, Y values are my income and X values are the work hours I put in. r

To calculate the ROC I would do the following.

(240 - 45) / (16 - 3) = 195 / 13 = 15% rate of change in my earnings between week 1 and week 2.

If you take the change in Y values and divide that with the change in X-values the result will be a rate of change,

In a graph of a value vs time, it would be the gradient. Otherwise simply divide the difference in any particular value by the time taken.

This is easier to work out from a graph, the rate of change is the gradient of the line - the change in y divided by the change in x. However, you might not have time in exam conditions to draw a graph when it's not asked of you, so I would suggest picking two points of the data - ignoring outliers if there are any. Calculate the difference between them by taking them away from each other, then divide that by the difference in time between them. This will give you the rate of change.

To find the rate of change, you typically calculate the difference in values of the quantity you’re measuring over a certain period of time or across a given interval. It is often expressed as a ratio of the change in the dependent variable to the change in the independent variable.

Formula:

The rate of change is commonly calculated using the formula:

\text{Rate of Change} = \frac{\text{Change in Output (y)}}{\text{Change in Input (x)}}

Where:

• y  is the dependent variable (output).

• x  is the independent variable (input).

Steps:

1. Identify the two points on the graph or in the data. These points are usually in the form of  (x_1, y_1)  and  (x_2, y_2) .

2. Calculate the difference between the two  y -values and  x -values.

• \Delta y = y_2 - y_1 

• \Delta x = x_2 - x_1 

3. Divide the change in  y  by the change in  x  to find the rate of change:

• \text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}

Example:

If the temperature increases from 10°C to 30°C over 4 hours, the rate of change in temperature is:

\text{Rate of Change} = \frac{30 - 10}{4 - 0} = \frac{20}{4} = 5 \, \text{°C per hour}

So, the temperature is increasing at a rate of 5°C per hour.

Derivatives are the best tool, but not for everyone... Considering two variables (distance and time, for example), you can also take the first and last value of both in a certain process, subtract the ones from the same variable (e.g. last and first distances of the bus from your position) and divide the subtractions of different variables. By doing this with position/distance and time, the rate of change you get is the speed of the object you're analyzing!