Question

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

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
because 0 sweaters knitted is
dollars earned.

Answer 1

the relationship has to be proprtional or non proportional

Answer 2

To answer your questions based on the data provided:

a. To find how many dollars are earned for every sweater knitted, we need to calculate the average earnings per sweater. We can use one of the data points as an example:

- For 7 sweaters, $392 earned:
$$\text{Dollars per sweater} = \frac{392}{7} = 56$$

So, to answer part (a): **Every sweater knitted is 56 dollars earned.**

b. The term used for "dollars per 1 sweater" is called a **rate**. Specifically, it can be named as the **unit rate**.

c. The relationship is **linear** because if we consider the case of 0 sweaters knitted (which is not listed in the data), the expected earnings would be $0.

Thus, to summarize:

a. Every sweater knitted is **56 dollars earned**.
b. Dollars/1 sweater is called a **rate**.
c. This relationship is **linear** because 0 sweaters knitted is **0 dollars earned**.

Answer 3

Thank you for the clarification! Given the context you provided, we can determine whether the relationship is proportional or non-proportional based on the definition of these terms:

- A **proportional relationship** means that as one quantity increases, the other quantity increases at a constant rate, which also includes the point when both quantities are zero (i.e., if you knit 0 sweaters, you earn $0).

- A **non-proportional relationship** means that the relationship does not pass through the origin (0,0) or that the ratio between the two quantities is not constant.

In your case, we see that:

- When 0 sweaters are knitted, the earnings would indeed be $0.
- The earnings per sweater are constant (56 dollars per sweater, as calculated).

Therefore, the relationship is **proportional** since it meets the criteria of passing through the origin (0,0) and maintaining a constant ratio.

So, to answer part (c): **This relationship is proportional because 0 sweaters knitted is 0 dollars earned.**