1. Given the table for x, sweater knitted, and y, money earned:
x: # of sweaters
y: $ earned
7
392
6
2
9
3
168
336
112
504
(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
a. Every sweater knitted is 56 dollars earned
b. Dollars/1 sweater is called a unit rate
c. This relationship is proportional because the ratio of dollars earned to sweaters knitted is consistent.
0 sweaters knitted is 0 dollars earned.
a. The constant of proportionality is
b. Write an equation that represents this graph
c. This is a proportional relationship because the y-intercept is
Search
a. The constant of proportionality is 56, since the ratio of dollars earned to sweaters knitted is consistently 56.
b. The equation that represents this graph is y = 56x, where y represents the dollars earned and x represents the number of sweaters knitted.
c. This is a proportional relationship because the y-intercept is 0.
To determine the relationship between the number of sweaters knitted and the money earned, let's analyze the data provided.
1. We have the following data points for x (number of sweaters) and y (money earned):
x: 7, 6, 2, 9, 3
y: 392, 168, 336, 112, 504
a. To find out how much money is earned for each sweater knitted, we can divide the money earned (y) by the number of sweaters knitted (x):
For the first data point:
Number of sweaters knitted (x) = 7
Money earned (y) = 392
392 / 7 = 56
For the second data point:
Number of sweaters knitted (x) = 6
Money earned (y) = 168
168 / 6 = 28
For the third data point:
Number of sweaters knitted (x) = 2
Money earned (y) = 336
336 / 2 = 168
For the fourth data point:
Number of sweaters knitted (x) = 9
Money earned (y) = 112
112 / 9 = 12.44 (approx.)
For the fifth data point:
Number of sweaters knitted (x) = 3
Money earned (y) = 504
504 / 3 = 168
Therefore,
a. Every sweater knitted is approximately $56, $28, $168, $12.44, and $168 (for each respective data point).
b. Dollars/1 sweater is called the "unit rate" or the "rate of change."
c. This relationship is a linear relationship because the ratio of dollars earned to sweaters knitted does not change. It is constant for each data point.
Finally, for the last part of the question, there is no information provided for when 0 sweaters are knitted. Hence, we cannot determine the dollars earned in that scenario.
To complete this exercise, we need to determine the relationship between the number of sweaters knitted (x) and the amount of money earned (y). Looking at the provided table, we can observe the following data points:
x: 7, 6, 2, 9, 3
y: 392, 168, 336, 112, 504
To find the relationship, we can analyze the data and look for any patterns or trends. One way to do this is by plotting the data on a graph and checking for a linear or non-linear relationship. However, since we only have five data points, it is difficult to draw any definitive conclusions just by looking at the graph.
Alternatively, we can calculate the ratio of money earned to the number of sweaters knitted (y/x) for each data point and see if there is a consistent value. Let's calculate this ratio for each data point:
For the first data point (x=7, y=392): 392/7 = 56
For the second data point (x=6, y=168): 168/6 = 28
For the third data point (x=2, y=336): 336/2 = 168
For the fourth data point (x=9, y=112): 112/9 ≈ 12.44
For the fifth data point (x=3, y=504): 504/3 = 168
Next, let's analyze the calculated ratios:
a. Every sweater knitted is approximately 56 dollars earned.
b. Dollars/1 sweater is called the "average earning per sweater."
c. This relationship is not linear because there is no consistent ratio between the number of sweaters and the money earned. For example, the ratio varies from 56 to 12.44 to 168.
d. 0 sweaters knitted would lead to no dollars earned since we see that there is no consistent ratio between the number of sweaters and the money earned.
To summarize:
a. Every sweater knitted is approximately 56 dollars earned.
b. Dollars/1 sweater is called the "average earning per sweater."
c. This relationship is not linear.
d. 0 sweaters knitted would result in no dollars earned.