Students can use the Spectrum Math Grade 8 Answer Key Chapter 4 Lesson 4.4 Functions and Nonlinear Relationships as a quick guide to resolve any of their doubts.
Spectrum Math Grade 8 Chapter 4 Lesson 4.4 Functions and Nonlinear Relationships Answers Key
Not all function tables represent a linear relationship. If the rate of change, or slope, is not constant, then the function does not represent a linear relationship.
Test the rate of change in a function table by using the slope formula, \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\), across multiple points on the table.
Find the rate of change, or slope, for points on the function table and decide if it represents a linear or nonlinear relationship.
Question 1.
a.
Relationship:
_________
Answer:
Linear.
Explanation:
The rate of change in a function table by using the slope formula, \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\), across multiple points on the table.
Slope (m) = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = Â \(\frac{-7-(-10)}{-5 – (-10)}\)
Rate = Â \(\frac{3}{5}\)
Rate = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = Â \(\frac{-1-(-4)}{-0 – (-5)}\)
Rate = Â \(\frac{3}{5}\)
b.
Relationship:
_________
Answer:
Linear.
Explanation:
The rate of change in a function table by using the slope formula, \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\), across multiple points on the table.
Slope (m) = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = Â \(\frac{-8-(-15)}{1 – (-3)}\)
Rate = Â \(\frac{7}{4}\)
Rate = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = Â \(\frac{6-(-1)}{9 – (5)}\)
Rate = Â \(\frac{7}{4}\)
Question 2.
a.
Relationship:
_________
Answer:
Nonlinear.
Explanation:
The rate of change in a function table by using the slope formula, \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\), across multiple points on the table.
Slope (m) = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = Â \(\frac{4-2}{1 – 0}\)
Rate = Â \(\frac{2}{1}\) = 2
Rate = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = Â \(\frac{28-10}{3 – 2}\)
Rate = Â \(\frac{18}{1}\) = 18
b.
Relationship:
_________
Answer:
Nonlinear.
-1, 1
Explanation:
The rate of change in a function table by using the slope formula, \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\), across multiple points on the table.
Slope (m) = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = Â \(\frac{5-6}{2-1}\)
Rate = Â \(\frac{-1}{1}\) = -1
Rate = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = Â \(\frac{5-4}{4-3}\)
Rate = Â \(\frac{1}{1}\) = 1
Question 3.
a.
Relationship:
_________
Answer:
Linear.
Explanation:
The rate of change in a function table by using the slope formula, \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\), across multiple points on the table.
Slope (m) = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = Â \(\frac{342-327}{20-10}\)
Rate = Â \(\frac{15}{10}\)
Rate = Â \(\frac{3}{2}\)
Rate = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = Â \(\frac{372-357}{40-30}\)
Rate = Â \(\frac{15}{10}\)
Rate = Â \(\frac{3}{2}\)
b.
Relationship:
_________
Answer:
Nonlinear.
Explanation:
The rate of change in a function table by using the slope formula, \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\), across multiple points on the table.
Slope (m) = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = Â \(\frac{102,000-100,000}{1-0}\)
Rate = Â \(\frac{2,000}{1}\) = 2,000
Rate = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
Rate = Â \(\frac{106,120-104,040}{3-2}\)
Rate = Â \(\frac{2,080}{1}\) = 2,080