We included **HMH Into Math Grade 8 Answer Key**** PDF** **Module 6 Understand and Analyze Functions **to make students experts in learning maths.

## HMH Into Math Grade 8 Module 6 Answer Key Understand and Analyze Functions

**Bead or No Bead**

A jeweler makes clay beads. To make the beads, different amounts of yellow clay and turquoise clay are mixed to make two new colors: lime and aqua. Lime has a greater ratio of yellow to turquoise than aqua does.

Fill in whether each mixture makes lime or aqua clay.

For each color, write an equation that models the relationship between the amounts of yellow clay y and turquoise clay t used to make it.

Lime: ____ Aqua: ____

Answer:

Lime = 4:3

Aqua = 3:2

**Turn and Talk**

How did you know which color each mixture produced?

**Are You Ready?**

**Complete these problems to review prior concepts and skills you will need for this module.**

**Represent Relationships with Variables**

**Identify the independent variable and the dependent variable for each situation.**

Question 1.

the relationship between the amount of water w a household uses and the cost of the household’s water bill b

independent: _____ dependent: _____

Answer:

amount of water w is independent

cost of the household’s water bill b is dependent

Question 2.

the relationship between the number of bags b of dog food a pet owner buys and the number of dogs d the pet owner has

independent: ____ dependent: _____

Answer:

given,

the relationship between the number of bags b of dog food a pet owner buys and the number of dogs d the pet owner has

number of bags b is dependent

number of dogs d is independent

**Model Proportional Relationships**

**Each table represents a proportional relationship. Write an equation to represent the relationship.**

Question 3.

Answer:

6:2 = 3:1

9:3 = 3:1

15:5 = 3:1

y = 1/3x

y = 1/3 × 6 = 2

y = 1/3 × 9 = 3

y = 1/3 × 15 = 5

So, the equation to represent the relationship is y = 1/3 x

Question 4.

Answer:

5:75 = 1:15

8:120 = 1:15

12:180 = 15

y = 15x

So, the equation to represent the relationship is y = 15x

**Graph Proportional Relationships**

**Graph each proportional relationship.**

Question 5.

y = 4x

Answer:

x = 0

y = 4(0) = 0

x = 1

y = 4(1) = 4

x = 2

y = 4(2) = 8

x = 3

y = 4(3) = 12

Question 6.

y = \(\frac{2}{3}\)x

Answer:

x = 0

y = \(\frac{2}{3}\)(0) = 0

x = 3

y = \(\frac{2}{3}\)(3) = 2

x = 6

y = \(\frac{2}{3}\)(6) = 4