University:
High School
Course:
High School Mathematics
Academic year:

2023
Views:

321

Pages:

4
Author:

anon

First Differences We learned how to identify linear and nonlinear relations through graphing in unit 3 (Chapter 2). Today, we will learn how to use tables of values (tcharts) to identify the typ e of relation. Example 1: Consider the relation y = 3x. a) Complete the table of values. x Y 0 0 1 3 2 6 3 9 4 12 b) Graph the relation. c) Classify the relation as linear or nonlinear. Linear d) Describe the pattern in the x-values. The values of x increase by a constant of 1. e) Add a third column to your table to record the change in y. Calculate eac h entry by subtracting consecutive values of y. The values in the third column are called first diff erences. f) What do you notice about the patterns in the third column? The first differences are the same (constant). Example 2: Use First Differences to determine if the following is linear or nonlinear This table of values represents a non-linear relation since the first differences are not the same This table of values represents a linear relation since the first differences are constant (equal). This table of values represents a non-linear relation since the since the first differences are not constant (equal) d) Match the following equations with the appropriate table above. 𝑥 𝑦 =2 2 𝑦 =𝑥 𝑦 =− 2𝑥 + 7 e) Write a rule for using first differences to determine whether a relation is linear or nonlinear A relation is linear if the first differences are constant (equal or the same). f) Describe how you can tell if the equation of a relation represents a linear relation. Linear - equation is of the form y= mx+b Or the highest degree of x is 1. Summary / Key Concepts: To work with first differences, the values of x (independent variable) must by a constant value. To find the first differences, subtract consecutive values of y(dep.var), 𝑛𝑑 starting with the 2 y-value. If the first differences of a relation are constant, the relation is linear. If the first differences of a relation are different, the relation is non-linear.