Sara graphs a line passing through points that represent a proportional relationship. Which set of points could be on the line that Sara graphs?
Responses
A (2, 4), (0, 2), (3, 9)(2, 4), (0, 2), (3, 9)
B (6, 8), (0, 0), (18, 24)(6, 8), (0, 0), (18, 24)
C (3, 6), (4, 8), (9, 4)(3, 6), (4, 8), (9, 4)
D (1, 1), (2, 1), (3, 3)(1, 1), (2, 1), (3, 3)
The correct set of points that could be on the line that Sara graphs is: A (2, 4), (0, 2), (3, 9)
u sure bro
I apologize for the incorrect response. Let me reassess the options for you.
A (2, 4), (0, 2), (3, 9): A line passing through these points would not have a constant rate of change and therefore would not represent a proportional relationship.
B (6, 8), (0, 0), (18, 24): These points do have a constant rate of change, where the y-value is twice the x-value. Therefore, this set of points could be on the line that Sara graphs and represents a proportional relationship.
C (3, 6), (4, 8), (9, 4): These points do not have a constant rate of change and therefore do not represent a proportional relationship.
D (1, 1), (2, 1), (3, 3): These points also have a constant rate of change, where the y-value is always equal to the x-value. Therefore, this set of points could also be on the line that Sara graphs and represents a proportional relationship.
Based on this reassessment, the correct options would be B and D. I apologize for the confusion caused by my initial response.
pick only one
In that case, the correct set of points that could be on the line that Sara graphs is:
B (6, 8), (0, 0), (18, 24)
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Question
Sam wants to know how long it will take to fill his baby pool that holds 24 gallons. After 1 minute, there are 2 gallons of water in the pool. He plots the points (0,0) and (1,2) on his coordinate plane. What is the x-value of the point (x, 24)?
Responses
A 66
B 1212
C 2323
D 25
To find the x-value of the point (x, 24), we need to determine how long it will take for Sam to fill the pool completely. Since after 1 minute there are 2 gallons of water in the pool, and the pool holds 24 gallons in total, we can set up a proportion to solve for x.
The ratio of gallons filled to time is constant: 2 gallons/1 minute = 24 gallons/x minutes.
To find x, we can cross-multiply and solve for x:
2x = 24 * 1
2x = 24
x = 12
Therefore, the x-value of the point (x, 24) is 12.
The correct answer is B: 1212.
Amount (Pounds) Price ($)
1 8
2 16
3 24
4 32
The cost for fudge at Sweet Treats is represented by y = 4x, where y is the price paid for x pounds. The table shows the cost of a similar fudge that Candy Lane sells.
Which statement is TRUE when comparing the stores' prices?
Responses
A The unit rate for fudge at Sweet Treats is twice the unit rate at Candy Lane.The unit rate for fudge at Sweet Treats is twice the unit rate at Candy Lane.
B The unit rate for fudge at Candy Lane is equal to the unit rate at Sweet Treats.The unit rate for fudge at Candy Lane is equal to the unit rate at Sweet Treats.
C The unit rate for fudge at Candy Lane is twice as much as the unit rate at Sweet Treats.The unit rate for fudge at Candy Lane is twice as much as the unit rate at Sweet Treats.
D The cost of 3 pounds of fudge at Sweet Treats is less than the cost of a pound of fudge at Candy Lane.The cost of 3 pounds of fudge at Sweet Treats is less than the cost of a pound of fudge at Candy Lane.
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The cost for fudge at Sweet Treats is represented by y = 4x, where y is the price paid for x pounds. Looking at the table, we can see that the unit rate for fudge at Sweet Treats is $4 per pound.
To find the unit rate for fudge at Candy Lane, we can observe that the price doubles with each pound. For example, when x = 1, the price is $8, and when x = 2, the price is $16. This means that for each additional pound, the price also increases by $8. Therefore, the unit rate for fudge at Candy Lane is $8 per pound.
Comparing the unit rates:
The unit rate for fudge at Sweet Treats is $4 per pound.
The unit rate for fudge at Candy Lane is $8 per pound.
Therefore, the correct statement is A: The unit rate for fudge at Sweet Treats is twice the unit rate at Candy Lane.