During a chemistry experiment, the pressure of a gas, in kilopascals (kPa), was recorded at one-minute intervals. The scatterplot shows the recorded pressure , in kPa, of the gas minutes after the start of the experiment. What was the average rate of change, in kPa per minute, of the recorded pressure of the gas from to ?

Solution available with step-by-step explanation

SAT Two-Variable Data Question 2 | Free SAT Prep | Aniko

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Question 2·Medium·Two-Variable Data: Models and Scatterplots

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During a chemistry experiment, the pressure of a gas, in kilopascals (kPa), was recorded at one-minute intervals. The scatterplot shows the recorded pressure $y$ , in kPa, of the gas $x$ minutes after the start of the experiment.

What was the average rate of change, in kPa per minute, of the recorded pressure of the gas from $x = 4$ to $x = 8$ ?

Your answer

(Express the answer as an integer)

For scatterplot questions asking for an average rate of change, immediately think "slope between two points." First, carefully read the $y$ -values at the given $x$ -coordinates from the plotted points. Then compute the change in $y$ (final minus initial) and the change in $x$ (final time minus initial time). Finally, divide change in $y$ by change in $x$ and keep the units (here, kPa per minute) in mind. Double-check that you didn’t stop after just subtracting the $y$ -values and that you used the correct time interval in the denominator.

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Locate the correct points on the scatterplot

Focus only on the data points above $x=4$ and $x=8$ . What pressures (the $y$ -values) do these points show?

Recall what "average rate of change" means

Average rate of change between two points on a graph is the slope of the line connecting them: change in $y$ divided by change in $x$ .

Calculate change in pressure and time

Subtract the pressure at 4 minutes from the pressure at 8 minutes to get the total change in pressure, and subtract 4 from 8 to get the change in time. Then divide the change in pressure by the change in time.

Desmos Guide

Enter the slope (rate of change) expression

After you read the pressure values at 4 and 8 minutes from the scatterplot, type an expression of the form (y8 - y4)/(8 - 4) into Desmos, replacing y8 and y4 with the actual pressures from the graph. For example, if the graph shows 30 kPa at 4 minutes and 54 kPa at 8 minutes, you would type (54 - 30)/(8 - 4).

Use the Desmos output as the rate

Look at the numerical value Desmos returns for that fraction. That value (in kPa per minute) is the average rate of change of the pressure between 4 and 8 minutes.

Step-by-step Explanation

Identify the two relevant data points

We are asked for the average rate of change from $x=4$ to $x=8$ minutes.

Look at the scatterplot and find the point whose $x$ -coordinate is 4; read its $y$ -value (pressure at 4 minutes). Call this $y_4$ .
Then find the point whose $x$ -coordinate is 8; read its $y$ -value (pressure at 8 minutes). Call this $y_8$ .

Compute the changes in pressure and in time

Average rate of change between two points is the slope of the line through them, which is

\text{average rate of change} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_8 - y_4}{8 - 4}.

From the scatterplot, the pressure at 8 minutes is 24 kPa greater than at 4 minutes, so $y_8 - y_4 = 24$ kPa. The time changes from 4 to 8 minutes, so $8 - 4 = 4$ minutes.

Divide to find the average rate of change

Now plug the values into the formula:

\text{average rate of change} = \frac{24}{4} = 6.

So, the average rate of change of the recorded pressure from $x=4$ to $x=8$ is $6$ kPa per minute.

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation