Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions

Students can use the Spectrum Math Grade 8 Answer Key Chapter 4 Lesson 4.5 Calculating Rate of Change in Functions as a quick guide to resolve any of their doubts.

Spectrum Math Grade 8 Chapter 4 Lesson 4.5 Calculating Rate of Change in Functions Answers Key

The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
Function tables can be used to find this rate of change.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 2
The rate of change for this function table is 4.

Find the rate of change for each function table. Write fractions in simplest form.

Question 1.
a.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 3
_______
Answer:
2

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{19 – 3}{10 – 2}\)
= \(\frac{16}{8}\) = 2

b.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 4
_______
Answer:
4

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{18 – 2}{4 – 0}\)
= \(\frac{16}{4}\) = 4

c.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 5
_______
Answer:
2

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{11 – 3}{4 – 0}\)
= \(\frac{8}{4}\) = 2

Question 2.
a.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 6
_______
Answer:
\(\frac{1}{2}\)

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{6.5 – 4.5}{5 – 1}\)
= \(\frac{2}{4}\)
= \(\frac{1}{2}\)

b.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 7
_______
Answer:
-8

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{-34 – (-2)}{5 – 1}\)
= \(\frac{-32}{4}\) =-8

c.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 8
_______
Answer:
-15

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{-20 – 40}{5 – 1}\)
= \(\frac{-60}{4}\) = -15

Question 3.
a.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 9
_______
Answer:
\(\frac{1}{3}\)

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{35 – 15}{90 – 30}\)
= \(\frac{20}{60}\)
= \(\frac{1}{3}\)

b.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 10
_______
Answer:
\(\frac{1}{6}\)

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{15}{90}\) – \(\frac{5}{30}\)
= \(\frac{10}{60}\)
= \(\frac{1}{6}\)

c.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 11
_______
Answer:
\(\frac{3}{2}\)

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{10-4}{4-0}\)
= \(\frac{6}{4}\)
= \(\frac{3}{2}\)

Find the rate of change for each function table. Write fractions in simplest form.

Question 1.
a.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 12
_______
Answer:
1

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{17-8}{12-3}\)
= \(\frac{9}{9}\) = 1

b.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 13
_______
Answer:
\(\frac{1}{9}\)

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{10-3}{90-27}\)
= \(\frac{7}{63}\)
= \(\frac{1}{9}\)

c.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 14
_______
Answer:
\(\frac{5}{4}\)

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{12-2}{14-6}\)
= \(\frac{10}{8}\)
= \(\frac{5}{4}\)

Question 2.
a.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 15
_______
Answer:
\(\frac{10}{3}\)

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{22-2}{8-2}\)
= \(\frac{20}{6}\)
= \(\frac{10}{3}\)

b.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 16
_______
Answer:
1

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{23-14}{12-3}\)
= \(\frac{9}{9}\) = 1

c.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 17
_______
Answer:
-1

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{-4-0}{12-8}\)
= \(\frac{-4}{4}\) = -1

Question 3.
a.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 18
_______
Answer:
\(\frac{9}{2}\)

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{45-9}{9-1}\)
= \(\frac{36}{8}\)
= \(\frac{9}{2}\)

b.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 19
_______
Answer:
2

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{14-10}{3-1}\)
= \(\frac{4}{2}\) = 2

c.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 20
_______
Answer:
\(\frac{1}{2}\)

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{2-0}{10-6}\)
= \(\frac{2}{4}\)
= \(\frac{1}{2}\)

Question 4.
a.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 21
_______
Answer:
\(\frac{1}{2}\)

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{-2-(-8)}{-6-6}\)
= \(\frac{6}{12}\)
= \(\frac{1}{2}\)

b.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 22
_______
Answer:
\(\frac{5}{6}\)

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{4-(-6)}{6-(-6)}\)
= \(\frac{10}{12}\)
= \(\frac{5}{6}\)

c.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 23
_______
Answer:
5

Explanation:
The rate of change that exists in a function can be calculated by finding the ratio of the amount of change in the output variable to the amount of change in the input variable.
Spectrum Math Grade 8 Chapter 4 Lesson 5 Answer Key Calculating Rate of Change in Functions 1
\(\frac{23-13}{4-2}\)
= \(\frac{10}{2}\) = 5

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