Given the table for x, sweater knitted, and y, money earned:

Question

x: # of sweaters 7 6 2 9 3
y: $ earned 392 336 112 504 168
(4 points)
a. Every sweater knitted is
dollars earned.

b. Dollars/1 sweater is called a
.

c. This relationship is

Answer 1

To analyze the relationship between the number of sweaters knitted (x) and the money earned (y), let's fill in the blanks.

a. Every sweater knitted is $
To find out how many dollars are earned for each sweater, we can calculate the ratio of total earnings to the number of sweaters knitted.

For example, for the first row (7 sweaters knitted, earning $392): \[ \frac{392}{7} = 56 \text{ dollars per sweater} \]

Doing this for all the provided data:

• For 7 sweaters: \( \frac{392}{7} = 56 \)
• For 6 sweaters: \( \frac{336}{6} = 56 \)
• For 2 sweaters: \( \frac{112}{2} = 56 \)
• For 9 sweaters: \( \frac{504}{9} = 56 \)
• For 3 sweaters: \( \frac{168}{3} = 56 \)

So, you can conclude:

a. Every sweater knitted is $56 earned.

---

b. Dollars/1 sweater is called a
This term is called a unit rate or unit price.

b. Dollars/1 sweater is called a unit rate.

---

c. This relationship is
The relationship between the number of sweaters knitted and the money earned is linear because the same amount ($56) is earned for each additional sweater, indicating a constant rate of change.

c. This relationship is linear.

To summarize:

• a. Every sweater knitted is $56 earned.
• b. Dollars/1 sweater is called a unit rate.
• c. This relationship is linear.

Answer 2

what
proportional

Answer 3

Thank you for your follow-up! Let's clarify the relationship based on your mention of "proportional."

In the context of the data provided (sweaters knitted and money earned), we can say that this relationship is proportional.

Explanation:

1. Proportional Relationship: A relationship is considered proportional if it can be expressed as a constant ratio (in this case, the same amount of money earned for each additional sweater). Since every sweater earns $56, the earnings are in direct proportion to the number of sweaters knitted.

2. Mathematical Representation: If you can express the relationship in the form \( y = kx \), where \( k \) is the constant of proportionality (in this case, \( k = 56 \)), then it is a proportional relationship.

Conclusion

So to complete the statement:

c. This relationship is proportional.

Hence, your summary would look like this:

• a. Every sweater knitted is $56 earned.
• b. Dollars/1 sweater is called a unit rate.
• c. This relationship is proportional.

This means that as you knit more sweaters, your earnings increase at a constant rate, which is characteristic of proportional relationships.

Answer 4

no is it proportional or
non proportional

Answer 5

The relationship between the number of sweaters knitted (x) and the money earned (y) is proportional.

Here’s why:

1. Constant Ratio: The amount earned per sweater is constant at $56. For each increase in the number of sweaters knitted, your earnings increase by a fixed dollar amount.

2. Direct Variation: The relationship can be expressed as \( y = kx \), where \( k \) is the constant of proportionality (in this case, \( k = 56 \)). Since there is a consistent multiplier throughout (every sweater earns $56), it satisfies the criteria for proportionality.

3. Origin Point (0,0): A proportional relationship can also be represented on a graph that passes through the origin (0,0). If you knitted 0 sweaters, you would earn $0, which aligns with the definition of direct proportionality.

Conclusion

Given the data you provided, this relationship is indeed proportional. If you have any further questions or need clarification, feel free to ask!