Let's analyze the information provided:
You have a set of data showing the relationship between the number of sweaters knitted (x) and the money earned (y):
- For 7 sweaters, $392 earned
- For 6 sweaters, $336 earned
- For 2 sweaters, $112 earned
- For 9 sweaters, $504 earned
- For 3 sweaters, $168 earned
Let's verify the statements one by one:
a. Every sweater knitted is 46 dollars earned.
To find the unit rate (dollars earned per sweater), divide the total money earned by the number of sweaters knitted for each data point:
- 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: \( \frac{168}{3} = 56 \)
In each case, the earnings per sweater is consistently $56, not $46.
Conclusion for (a):
False. Every sweater knitted earns $56, not $46.
b. Dollars/1 sweater is called a unit rate.
The definition of a unit rate is indeed the amount earned (or another quantity) for one unit of something—in this case, dollars per one sweater. Since we calculated earlier that it is $56/sweater:
Conclusion for (b):
True. The amount earned per sweater is indeed called a unit rate.
c. This relationship is proportional because 0 sweaters knitted is dollars earned.
A proportional relationship means that there is a consistent ratio between two quantities. One key characteristic is that if one quantity is zero, the other must also be zero (which corresponds to the origin point (0,0) on a graph).
Since when 0 sweaters are knitted, the money earned is $0, this satisfies the condition for proportionality. Furthermore, the constant unit rate of $56/sweater supports that this is a proportional relationship because:
- The relationship can be expressed as \( y = 56x \), where \( y \) is the money earned, and \( x \) is the number of sweaters knitted.
Conclusion for (c):
True. The relationship is proportional since earning is $0 when no sweaters are knitted.
Summary:
- (a) False: Every sweater knitted earns $56, not $46.
- (b) True: Dollars per 1 sweater is called a unit rate.
- (c) True: The relationship is proportional because 0 sweaters knitted results in $0 earned.
3 answers