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
