Question
The table and graph show that there are 32 ounces in a quart.
Conversion between Quarts and Ounces
Ounces
(x)
Quarts
(y)
8
0.25
16
0.5
32
1
40
1.25
On a coordinate plane, the x-axis is labeled Ounces and the y-axis is labeled quarts. The line goes through points (8, 0.25) and (16, 0.5).
Which statement about the graph is true?
The number of quarts is the independent variable, and the number of ounces is the dependent variable.
The point (56, 1.75) is on the line.
The number of ounces is graphed on the y-axis, and the number of quarts is graphed on the x-axis.
The two variables are the number of quarts and the number of ounces in a quart.
Conversion between Quarts and Ounces
Ounces
(x)
Quarts
(y)
8
0.25
16
0.5
32
1
40
1.25
On a coordinate plane, the x-axis is labeled Ounces and the y-axis is labeled quarts. The line goes through points (8, 0.25) and (16, 0.5).
Which statement about the graph is true?
The number of quarts is the independent variable, and the number of ounces is the dependent variable.
The point (56, 1.75) is on the line.
The number of ounces is graphed on the y-axis, and the number of quarts is graphed on the x-axis.
The two variables are the number of quarts and the number of ounces in a quart.
Answers
GPT-4o mini
To determine which statement about the graph is true, let's analyze each statement based on the information provided.
1. **The number of quarts is the independent variable, and the number of ounces is the dependent variable.**
This statement is true. In the context of conversion, the quarts (y) are considered the independent variable, while ounces (x) depend on how many quarts are present.
2. **The point (56, 1.75) is on the line.**
To check this, we can convert quarts to ounces for 1.75 quarts:
\( 1.75 \, \text{quarts} \times 32 \, \text{ounces/quart} = 56 \, \text{ounces} \).
So, this point is indeed on the line. This statement is also true.
3. **The number of ounces is graphed on the y-axis, and the number of quarts is graphed on the x-axis.**
According to the description, the x-axis is labeled with ounces and the y-axis with quarts. Therefore, this statement is false.
4. **The two variables are the number of quarts and the number of ounces in a quart.**
The phrase "the number of ounces in a quart" is misleading, as this suggests a relationship that doesn’t directly align with the independent/dependent variable structure. Therefore, this statement is also false.
Based on these evaluations, statements 1 and 2 are true, while statements 3 and 4 are false. The strongest and most straightforward statement is **1**, as it correctly defines the independent and dependent variables in this context.
1. **The number of quarts is the independent variable, and the number of ounces is the dependent variable.**
This statement is true. In the context of conversion, the quarts (y) are considered the independent variable, while ounces (x) depend on how many quarts are present.
2. **The point (56, 1.75) is on the line.**
To check this, we can convert quarts to ounces for 1.75 quarts:
\( 1.75 \, \text{quarts} \times 32 \, \text{ounces/quart} = 56 \, \text{ounces} \).
So, this point is indeed on the line. This statement is also true.
3. **The number of ounces is graphed on the y-axis, and the number of quarts is graphed on the x-axis.**
According to the description, the x-axis is labeled with ounces and the y-axis with quarts. Therefore, this statement is false.
4. **The two variables are the number of quarts and the number of ounces in a quart.**
The phrase "the number of ounces in a quart" is misleading, as this suggests a relationship that doesn’t directly align with the independent/dependent variable structure. Therefore, this statement is also false.
Based on these evaluations, statements 1 and 2 are true, while statements 3 and 4 are false. The strongest and most straightforward statement is **1**, as it correctly defines the independent and dependent variables in this context.