SAT Two-Variable Data Question 42 | Free SAT Prep | Aniko

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Question 42·Hard·Two-Variable Data: Models and Scatterplots

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The scatterplot shows the time $x$ (in hours) that a crystal was left in a solution and the mass $y$ (in milligrams) of the crystal at the end of the time for 9 trials. The line of best fit for the data is also shown.

Using the slope of the line of best fit, which choice is closest to the crystal’s average growth rate, in micrograms per minute?

(Use $1$ milligram $=1{,}000$ micrograms and $1$ hour $=60$ minutes.)

For scatterplot best-fit questions, read two convenient points on the best-fit line to find the slope (rate of change). Then track units carefully: the slope gives “change in $y$ per change in $x$ ,” so convert that rate into the requested units by multiplying by conversion factors that cancel units.

Hints

Click me!

Pick points on the line (not the dots)

Choose two grid-intersection points that the line of best fit passes through.

Slope units matter

Compute $\frac{\Delta y}{\Delta x}$ to get milligrams per hour (mg/hour).

Convert the rate

Multiply by $1{,}000$ to change mg to micrograms, then divide by $60$ to change “per hour” to “per minute.”

Desmos Guide

Enter two points from the best-fit line

Use points on the line such as $(2,15)$ and $(8,55)$ .

Compute the slope (mg/hour)

In Desmos, enter (55-15)/(8-2).

Convert to micrograms per minute

Multiply the slope by 1000/60.

Match to the closest choice

Compare the computed value to the four answer choices and select the closest one.

Step-by-step Explanation

Use two points on the best-fit line

Use two clear grid-intersection points on the line of best fit. From the graph, the line passes through $(2,15)$ and $(8,55)$ , where $x$ is hours and $y$ is milligrams.

Compute the slope in milligrams per hour

\text{slope}=\frac{55-15}{8-2}=\frac{40}{6}=\frac{20}{3}\ \text{mg/hour}.

Convert milligrams per hour to micrograms per minute

First convert mg to micrograms, then hours to minutes:

\frac{20}{3}\ \frac{\text{mg}}{\text{hour}}\cdot \frac{1{,}000\ \mu\text{g}}{1\ \text{mg}}=\frac{20{,}000}{3}\ \frac{\mu\text{g}}{\text{hour}}.

\frac{20{,}000}{3}\ \frac{\mu\text{g}}{\text{hour}}\cdot \frac{1\ \text{hour}}{60\ \text{min}}=\frac{20{,}000}{180}\approx 111.1\ \frac{\mu\text{g}}{\text{min}}.

Choose the closest option

$111.1$ micrograms per minute is closest to $111$ .

Answer: $111$

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation