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Isabella filled a pool with water, and modeled the relationship between the time since she started filling the pool

\[T\] (in minutes) and the amount of water in the pool
\[W\] (in liters) as
\[W=135T\].
She wanted to graph the relationship until the pool is full, which is when there are
\[16{,}000\] liters of water. Here is her work:
A line increasing as x increases on an x y coordinate plane. The x axis scales by twelve from zero to one hundred twenty. The y axis scales by two thousand from zero to eighteen thousand. The y axis is labeled Water in liters. The x axis is labeled time in minutes. The line starts at the y axis at (zero, zero) passing through the point around (sixty, eight thousand) before reaching around (one hundred twenty, sixteen thousand).
\[\small{12}\]
\[\small{24}\]
\[\small{36}\]
\[\small{48}\]
\[\small{60}\]
\[\small{72}\]
\[\small{84}\]
\[\small{96}\]
\[\small{108}\]
\[\small{2000}\]
\[\small{4000}\]
\[\small{6000}\]
\[\small{8000}\]
\[\small{10{,}000}\]
\[\small{12{,}000}\]
\[\small{14{,}000}\]
\[\small{16{,}000}\]
What mistakes did Isabella 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

1 answer

To determine the mistakes Isabella made when drawing the graph, we can analyze the information given:

  1. The equation for the amount of water in the pool is \( W = 135T \), which means that for every minute (\( T \)) that passes, 135 liters of water are added to the pool.

  2. The pool reaches its full capacity at 16,000 liters. To find out how long it takes to fill the pool, we can set \( W = 16,000 \): \[ 16,000 = 135T \implies T = \frac{16,000}{135} \approx 118.52 \text{ minutes} \]

  3. Based on the calculation, the time \( T \) needed to fill the pool completely is approximately 118.52 minutes, which means that the graph should extend beyond 120 minutes on the x-axis to accurately represent the time it takes to fill the pool.

  4. The y-axis scales from 0 to 18,000 liters, which is appropriate as it includes the maximum water amount of 16,000 liters.

  5. The x-axis, however, appears to range from 0 to 120 minutes. Since the calculated time to fill the pool exceeds 120 minutes, the scale on the x-axis is inappropriate.

With this analysis, let's evaluate the choices given:

  • (Choice A) Inappropriate scale for \( x \)-axis: Correct. The graph should extend beyond 120 minutes.
  • (Choice B) Inappropriate scale for \( y \)-axis: Incorrect. The y-axis scale is appropriate as it goes up to 18,000.
  • (Choice C) Wrong/missing label for \( x \)-axis: Incorrect. The x-axis is labeled properly as "time in minutes."
  • (Choice D) Wrong/missing label for \( y \)-axis: Incorrect. The y-axis is labeled correctly as "Water in liters."

The correct answer is:

  • (Choice A) Inappropriate scale for \( x \)-axis