How do you find the rate of change?

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.

Distance traveled divided by time it takes. On a graph that would be calculating the difference in the change in y and the change in x

Rate of change is essentially the change in the dependent variable (y axis) over the change in the independent variable (x axis). It is how much one quantity e.g velocity changes with respect to another e.g time. All you have to do is figure out the gradient at the point you are trying to find the rate of change at! This gradient is the y/x e.g acceleration.

Consider the following equation

y=mx+c

The changing quantity is represented by the letter "y" called the independent variable. It is dependent upon a variable called the dependent variable denoted by 'x'. Find the value of "y" at two values of x. let Y1 be the output of X1 and Y2 be the output of X2. The rate of change of y will be calculated as follows:

dy/dx= (Y2-Y1)/(X2-X1)

Referring to a straight line graph, the rate of change can be found using the formula: change in y/change in x, practically speaking, When dealing with a straight line, it's best to "make a right angled triangle" choosing points appropriately. Your result is the "gradient" or "slope" of the line which tells you the rate of change. It can either be positive, negative or 0 if the straight line is parallel to the x axis.

The rate of change (ROC) is the speed at which a variable changes over a specific period of time

If we have a graph, the rate of change at a particular point is the gradient of the tangent at that point - this is known as the derivative. Given some values, we could approximate the rate of change by calculating the gradient of the graph of those values at that point i.e. rise over run

This is an easy thing to find out. If you have a straight line on a X-Y graph, the formula you would use is y=mx+c. The rate of change is m in this formula is is how steep the line is . To calculate m for this formula you choose two separate points on the line (taking note of their X-Y coordinates). Then you take the difference between the y coordinates then take the difference between the x coordinates. Then you take these two numbers and divide the difference between the y coordinates by the difference between the x coordinates. This will give you the steepness of the line which is m in the formula of a straight line.

The rate of change can be found by calculating the difference in the values of a quantity over a certain period of time or another variable. It is often calculated using the formula:

Rate of change = (Change in quantity) / (Change in time or another variable)

For example, to find the rate of change of distance with respect to time, you would divide the change in distance by the change in time. This gives you the speed or velocity.

The rate of change refers to what degree a variable relates to another.

Considering two points connected by a line on an XY graph. The rate of change of the variable Y in relation to X can be calculated by finding the gradient. The gradient = the change in Y, divided by, the change in X.

For example, given a line graph of distance travelled against time, the average gradient between two points along the graph can be found by: gradient = distance1-distance2/time1-time2. This also represents the speed between time1 and time2, as speed is defined as the rate of change of distance.

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.

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)

Hi Vickie,

The rate of change is usually obtained if you divide by time.

Derivative with respect to another variable

We can find the rate of change by calculating the gradient of the curve or line. We identify two points on the line. Next we find the difference in the y-axis points and divide by the difference in the x-axis points. E.g. (Y2 - Y1)/(X2 - X1)