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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.

3 answers

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.

the relationship has to be proprtional or non proportional

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.