# Spectrum Math Grade 8 Chapter 4 Lesson 4 Answer Key Functions and Nonlinear Relationships

Students can use the Spectrum Math Grade 8 Answer Key Chapter 4 Lesson 4.4 Functions and Nonlinear RelationshipsÂ 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:
_________
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:
_________
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:
_________
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:
_________
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:
_________
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:
_________
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

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