Rate of Change and Slope
Standard
F.LE.1.b Recognize situations in which one quantity changes at a constant rate relative to another.
Goals for this section:
Students will learn what the concept of rate of change is. Conceptually, the rate of change of a graph is how "fast" a graph is increasing. The rate of change is also just the slope between two points.
To use the equation, we need two coordinates from the graph which we designate as:
The subscripts (the little numbers that are lowered) are ways to designate which point is first and which one is second. They're just "names".
It doesn't matter which points you choose as first or second so long as they're different points on the line. Sometimes the points are just given to you.
Example 1
Given (2, 4) and (-6, 6), find the slope.
Suggestion 1. Label your coordinates! You can write it underneath the coordinates like so:
Suggestion 2. Write down the formula for your reference! When you write the formula down, you're more likely to remember it. Then plug in your values.
Example 2
Given (4, 5) and (3, 3), find the slope.
Average Rate of Change
The Average Rate of Change between two points is just the slope.
Consider this graph:
Look from the interval x = 0 to x = 1. The graph is steeper during this interval, it rises faster, and the rate of change is faster.
Look from the interval x = 1.5 to x = 2. The graph isn't as steep, it rises much more slowly, and the rate of change is slower.
This is the concept behind the Average Rate of Change. It is an approximation of how much a graph increases or decreases from one point to another.
If you are asked for a Rate of Change, know that it's just a slope.
- You most likely will be given two points in some form (either given to you or you must figure out the points) and then you use the slope formula to find the Average Rate of Change.
The Rate of Change can also be used for piecewise functions. It is expressed as f(b)-f(a)
External Resources
A basic introduction into what the average rate of change is.
This video will show you how to take information from a table and find the rate of change for it.
How to use the rate of change formula to find the rate of change.
Olmos math 1 August 25, 2020 week 4 day 1.pdf