Rates of Change
Key Questions

Answer:
As below.
Explanation:
Slope is the ratio of the vertical and horizontal changes between two points on a surface or a line.
The vertical change between two points is called the rise, and the horizontal change is called the run.
The slope equals the rise divided by the run: .
This simple equation is called the slope formula.If
#y = f(x+h) = 3 (x + h)^ 2# , (Just plug x + h in for x). So, you get this:The instantaneous rate of change, or derivative, can be written as dy/dx, and it is a function that tells you the instantaneous rate of change at any point.
#y' = f'(x+h) = (d/(dx)) (3*(x)^2) = 6x * 1 = 6x# . For example, if x = 1, then the instantaneous rate of change is 6.
Rate of Change Formula helps us to calculate the slope of a line if the coordinates of the points on the line are given. ... If coordinates of any two points of a line are given, then the rate of change is the ratio of the change in the ycoordinates to the change in the xcoordinates.
Hope this helps.

Rate of change is a number that tells you how a quantity changes in relation to another.
Velocity is one of such things. It tells you how distance changes with time.
For example: 23 km/h tells you that you move of 23 km each hour.Another example is the rate of change in a linear function.
Consider the linear function:
#y=4x+7#
the number 4 in front of#x# is the number that represent the rate of change. It tells you that every time#x# increases of 1, the corresponding value of#y# increases of 4.
If you get a negative number it means that the#y# value is decreasing.
If the number is zero it means that you do not have change, i.e you have a constant!Examples:

Average Rate of Change
The average rate of change of a function
#f(x)# on an interval#[a,b]# can be found by#("Average Rate of Change")={f(b)f(a)}/{ba}#
Example
Find the average rate of change of
#f(x)=x^2+3x# on#[1,3]# .#f(3)=(3)^2+3(3)=18# #f(1)=(1)^2+3(1)=4# #("Average Rate of Change")={f(3)f(1)}/{31}={184}/{2}=14/2=7#
I hope that this was helpful.
Questions
Graphs of Linear Equations and Functions

Graphs in the Coordinate Plane

Graphs of Linear Equations

Horizontal and Vertical Line Graphs

Applications of Linear Graphs

Intercepts by Substitution

Intercepts and the CoverUp Method

Slope

Rates of Change

SlopeIntercept Form

Graphs Using SlopeIntercept Form

Direct Variation

Applications Using Direct Variation

Function Notation and Linear Functions

Graphs of Linear Functions

Problem Solving with Linear Graphs