Question
Sean drank a slushy as fast as he could. He modeled the relationship between the time since he started drinking
\[T\] (in seconds) and the remaining amount of slushy
\[S\] (in milliliters) as
\[S=600-7.5T\].
He wanted to graph the relationship from the moment he started drinking until he finished the slushy. Here is his work:
A line decreasing as x increases on an x y coordinate plane. The x axis scales by twenty from zero to one hundred sixty. The y axis scales by two hundred. The y axis is labeled slushy in liters. The x axis is labeled time in seconds. The line starts at the y axis at (zero, six hundred) passing through the point (forty, ten) before reaching the x axis at (eighty, zero).
\[\small{20}\]
\[\small{40}\]
\[\small{60}\]
\[\small{80}\]
\[\small{100}\]
\[\small{120}\]
\[\small{140}\]
\[\small{200}\]
\[\small{400}\]
\[\small{600}\]
\[\small{800}\]
\[\small{1000}\]
\[\small{1200}\]
\[\small{1400}\]
\[\small{1600}\]
\[\small{1800}\]
What mistakes did Sean make when drawing the graph?
Choose all answers that apply:
Choose all answers that apply:
(Choice A) Inappropriate scale for
\[x\]-axis
A
Inappropriate scale for
\[x\]-axis
(Choice B) Inappropriate scale for
\[y\]-axis
B
Inappropriate scale for
\[y\]-axis
(Choice C) Wrong/missing label for
\[x\]-axis
C
Wrong/missing label for
\[x\]-axis
(Choice D) Wrong/missing label for
\[y\]-axis
D
Wrong/missing label for
\[y\]-axis
(Choice E) Sean didn't make any mistake
E
Sean didn't make any mistake
\[T\] (in seconds) and the remaining amount of slushy
\[S\] (in milliliters) as
\[S=600-7.5T\].
He wanted to graph the relationship from the moment he started drinking until he finished the slushy. Here is his work:
A line decreasing as x increases on an x y coordinate plane. The x axis scales by twenty from zero to one hundred sixty. The y axis scales by two hundred. The y axis is labeled slushy in liters. The x axis is labeled time in seconds. The line starts at the y axis at (zero, six hundred) passing through the point (forty, ten) before reaching the x axis at (eighty, zero).
\[\small{20}\]
\[\small{40}\]
\[\small{60}\]
\[\small{80}\]
\[\small{100}\]
\[\small{120}\]
\[\small{140}\]
\[\small{200}\]
\[\small{400}\]
\[\small{600}\]
\[\small{800}\]
\[\small{1000}\]
\[\small{1200}\]
\[\small{1400}\]
\[\small{1600}\]
\[\small{1800}\]
What mistakes did Sean make when drawing the graph?
Choose all answers that apply:
Choose all answers that apply:
(Choice A) Inappropriate scale for
\[x\]-axis
A
Inappropriate scale for
\[x\]-axis
(Choice B) Inappropriate scale for
\[y\]-axis
B
Inappropriate scale for
\[y\]-axis
(Choice C) Wrong/missing label for
\[x\]-axis
C
Wrong/missing label for
\[x\]-axis
(Choice D) Wrong/missing label for
\[y\]-axis
D
Wrong/missing label for
\[y\]-axis
(Choice E) Sean didn't make any mistake
E
Sean didn't make any mistake
Answers
GPT-4o mini
Let's analyze Sean's work regarding the graph of the relationship between time \( T \) (in seconds) and the remaining amount of slushy \( S \) (in milliliters).
1. **Equation Check**: The equation given is \( S = 600 - 7.5T \). This indicates that the initial amount of slushy is 600 mL and that it decreases by 7.5 mL for every second that passes.
2. **Finding Time to Finish**: To find out when Sean finishes the slushy, we set \( S = 0 \):
\[
0 = 600 - 7.5T \implies 7.5T = 600 \implies T = \frac{600}{7.5} = 80 \text{ seconds}.
\]
This confirms that Sean should be finished after 80 seconds.
3. **Y-Axis Scale**: The maximum value of \( S \) is 600 mL at \( T = 0 \) seconds, and it decreases to 0 mL at 80 seconds. Sean stated that the y-axis is scaled by 200 and labeled in liters. The amount of slushy was initially 600 mL, which is 0.6 liters, but it seems like he plotted it incorrectly. Thus, he should label the axis in milliliters instead of liters.
4. **X-Axis Scale**: The x-axis represents time in seconds. Since he starts at \( T = 0 \) and ends at \( T = 80 \), the scale of the x-axis from 0 to 160 seconds is unnecessary, as a scale up to 80 seconds would be sufficient.
5. **Labeling**: The x-axis should be labeled appropriately as "Time (seconds)" and the y-axis as "Remaining Slushy (mL)" if he's using milliliters as the unit.
Now, let's review the choices based on this analysis:
- **(Choice A)** Inappropriate scale for the \( x \)-axis: **True** since 0 to 160 seconds is unnecessary.
- **(Choice B)** Inappropriate scale for the \( y \)-axis: **True** since it should be labeled in milliliters (mL) instead of liters, and the scaling does not correctly reflect the values.
- **(Choice C)** Wrong/missing label for the \( x \)-axis: **False** (not specified in the problem, but the labeling of the x-axis as time in seconds seems reasonable based on context).
- **(Choice D)** Wrong/missing label for the \( y \)-axis: **True** since it should reflect milliliters, not liters.
- **(Choice E)** Sean didn't make any mistake: **False**.
Thus, the correct choices are:
- **(Choice A)** Inappropriate scale for the \( x \)-axis
- **(Choice B)** Inappropriate scale for the \( y \)-axis
- **(Choice D)** Wrong/missing label for the \( y \)-axis
1. **Equation Check**: The equation given is \( S = 600 - 7.5T \). This indicates that the initial amount of slushy is 600 mL and that it decreases by 7.5 mL for every second that passes.
2. **Finding Time to Finish**: To find out when Sean finishes the slushy, we set \( S = 0 \):
\[
0 = 600 - 7.5T \implies 7.5T = 600 \implies T = \frac{600}{7.5} = 80 \text{ seconds}.
\]
This confirms that Sean should be finished after 80 seconds.
3. **Y-Axis Scale**: The maximum value of \( S \) is 600 mL at \( T = 0 \) seconds, and it decreases to 0 mL at 80 seconds. Sean stated that the y-axis is scaled by 200 and labeled in liters. The amount of slushy was initially 600 mL, which is 0.6 liters, but it seems like he plotted it incorrectly. Thus, he should label the axis in milliliters instead of liters.
4. **X-Axis Scale**: The x-axis represents time in seconds. Since he starts at \( T = 0 \) and ends at \( T = 80 \), the scale of the x-axis from 0 to 160 seconds is unnecessary, as a scale up to 80 seconds would be sufficient.
5. **Labeling**: The x-axis should be labeled appropriately as "Time (seconds)" and the y-axis as "Remaining Slushy (mL)" if he's using milliliters as the unit.
Now, let's review the choices based on this analysis:
- **(Choice A)** Inappropriate scale for the \( x \)-axis: **True** since 0 to 160 seconds is unnecessary.
- **(Choice B)** Inappropriate scale for the \( y \)-axis: **True** since it should be labeled in milliliters (mL) instead of liters, and the scaling does not correctly reflect the values.
- **(Choice C)** Wrong/missing label for the \( x \)-axis: **False** (not specified in the problem, but the labeling of the x-axis as time in seconds seems reasonable based on context).
- **(Choice D)** Wrong/missing label for the \( y \)-axis: **True** since it should reflect milliliters, not liters.
- **(Choice E)** Sean didn't make any mistake: **False**.
Thus, the correct choices are:
- **(Choice A)** Inappropriate scale for the \( x \)-axis
- **(Choice B)** Inappropriate scale for the \( y \)-axis
- **(Choice D)** Wrong/missing label for the \( y \)-axis