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

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

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: ____
Lime = 4:3
Aqua = 3:2

Turn and Talk
How did you know which color each mixture produced?

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: _____
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: _____
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.

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.

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

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

y = $$\frac{2}{3}$$(0) = 0
y = $$\frac{2}{3}$$(3) = 2
y = $$\frac{2}{3}$$(6) = 4