This handy Spectrum Math Grade 7 Answer Key Chapter 4 Lesson 4.3 Constants of Proportionality provides detailed answers for the workbook questions.
Spectrum Math Grade 7 Chapter 4 Lesson 4.3 Constants of Proportionality Answers Key
A unit rate can also be called a constant of proportionality. The constant of proportionality describes the rate at which variables in an equation change.
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 6 ÷ 2 = 3; 9 ÷ 3 = 3; 15 ÷ 5 = 3; k = 3
Find the constant of proportionality for each set of values.
Question 1.
a.
k = _____
Answer: 1.5
k = 1.5
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 1.5 ÷ 1 = 1.5 ,
3 ÷ 2 = 1.5 ,
4.5 ÷ 3 = 1.5 ,
12 ÷ 8 = 1.5 ,
Therefore, k = 1.5
b.
k = _____
Answer: 5
k = 5
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 2 ÷ 0.4 = 5 ,
4 ÷ 0.8 = 5 ,
7 ÷ 1.4 = 5 ,
9 ÷ 1.8 = 5
Therefore, k = 5
Question 2.
a.
k = _____
Answer: 2
k = 2
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 2 ÷ 1 = 2 ,
4 ÷ 2 = 2 ,
5 ÷ 2.5 = 2 ,
7 ÷ 3.5 = 2
Therefore, k = 2
b.
k = _____
Answer: 1.67
k = 1.67
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 7.5 ÷ 4.5 = 1.67 ,
10 ÷ 6 = 1.67 ,
17.5 ÷ 10.5 = 1.67 ,
20 ÷ 12 = 1.67
Therefore, k = 1.67
Question 3.
a.
k = _____
Answer: 0.5
k = 0.5
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 1 ÷ 2 = 0.5 ,
2 ÷ 4 = 0.5 ,
3 ÷ 6 = 0.5 ,
4 ÷ 8 = 0.5
Therefore, k = 0.5
b.
k = _____
Answer: 0.2
k = 0.2
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 2 ÷ 10 = 0.2 ,
4 ÷ 20 = 0.2 ,
6 ÷ 30 = 0.2 ,
8 ÷ 40 = 0.2
Therefore, k = 0.2
Find the constant oí proportionality for each set of values.
Question 1.
a.
k = _____
Answer: 2
k = 2
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 2 ÷ 1 = 2 ,
4 ÷ 2 = 2 ,
6 ÷ 3 = 2 ,
8 ÷ 4 = 2
Therefore, k = 2
b.
k = _____
Answer: 0.67
k = 0.67
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 2 ÷ 3 = 0.67 ,
4 ÷ 6 = 0.67 ,
6 ÷ 9 = 0.67 ,
8 ÷ 12 = 0.67
Therefore, k = 0.67
Question 2.
a.
k = _____
Answer: 0.2
k = 0.2
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 1 ÷ 5 = 0.2 ,
3 ÷ 15 = 0.2 ,
5 ÷ 25 = 0.2,
7 ÷ 35 = 0.2
Therefore, k = 0.2
b.
k = _____
Answer: 0.8
k = 0.8
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 4 ÷ 5 = 0.8 ,
8 ÷ 10 = 0.8 ,
12 ÷ 15 = 0.8 ,
20 ÷ 25 = 0.8
Therefore, k = 0.8
Question 3.
a.
k = _____
Answer: 0.167
k = 0.167
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 3 ÷ 18 = 0.167 ,
5 ÷ 30 = 0.167 ,
7 ÷ 42 = 0.167 ,
9 ÷ 54 = 0.167
Therefore, k = 0.167
b.
k = _____
Answer: 2
k = 2
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 0.5 ÷ 0.25 = 2 ,
2 ÷ 1 = 2 ,
6 ÷ 3 = 2 ,
8 ÷ 4 = 2
Therefore, k = 2
Question 4.
a.
k = _____
Answer: 0.25
k = 0.25
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 1 ÷ 4 = 0.25 ,
2 ÷ 8 = 0.25 ,
3 ÷ 12 = 0.25 ,
4 ÷ 16 = 0.25
Therefore, k = 0.25
b.
k = _____
Answer: 0.75
k = 0.75
Step 1: Set up an equation in which the constant (k) is equal to y ÷ x.
Step 2: Check the equation across multiple points to verify the constant.
Step 3: 3 ÷ 4 = 0.75 ,
6 ÷ 8 = 0.75 ,
9 ÷ 12 = 0.75 ,
12 ÷ 16 = 0.75
Therefore, k = 0.75