Question 1·SAT Desmos Regression Practice·Problem Solving and Data Analysis

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The scatterplot shows the relationship between the number of minutes after a cup of tea is poured, $x$ , and the temperature of the tea (in degrees Celsius), $y$ .

Which value is closest to the slope of a line of best fit for the data?

A line of best fit follows the overall straight trend of a scatterplot; it doesn't have to pass through every dot. Its slope tells you how much the temperature changes per minute, so a downward trend needs a negative slope. Enter the plotted pairs in a Desmos table and fit a line, then read its slope. Don't mistake the total temperature drop for the drop in one minute.

Hints

Hint 1
The slope is the temperature change for one more minute. The dots fall as you move right, so what sign should the fitted line's slope have?
Hint 2
A line of best fit summarizes all the dots, even if it misses some of them. Put each dot's minute in $x_1$ and its temperature in $y_1$ , keeping the two values in the same row.
Hint 3
In $y_1\sim mx_1+b$ , $m$ is the slope. Desmos reports its fitted value under PARAMETERS. Which answer is closest to that value?

Step-by-step

Approach 1: Fit a line in Desmos
Step 1
Enter the plotted pairs
Read minutes from the horizontal axis and temperature from the vertical axis. The six dots are $(0,19)$ , $(1,16)$ , $(2,14)$ , $(3,10)$ , $(4,8)$ , and $(5,4)$ . Enter them as matching rows in a Desmos table, with minutes in $x_1$ and temperatures in $y_1$ . The dots fall from left to right, so expect a negative slope.
Step 2
Fit the straight trend
Type $y_1\sim mx_1+b$ below the table. The $\sim$ tells Desmos to run a linear regression, finding the straight line that best fits all six dots. Under PARAMETERS, Desmos reports $m\approx-2.94$ . Here $m$ is the slope: the fitted temperature change for each extra minute.
Step 3
Choose the closest slope
The fitted temperature changes by about $-2.94$ degrees Celsius per minute, so the closest value is $-3$ . Slope is the change per minute, not the total change across the graph. Choice B.

Approach 2: Estimate from distant dots
Step 1
Pick dots far apart in time
The dots at $(0,19)$ and $(5,4)$ are far apart, and the other dots stay near the straight path between them. Their rate gives a quick estimate of the slope of a line of best fit. The fitted line itself doesn't have to pass through either dot.
Step 2
Find the temperature change per minute
Slope is temperature change divided by time change. Type $\frac{4-19}{5-0}$ in Desmos; it prints $-3$ . This is an estimate from two dots, rather than the exact fitted slope, and it gives the closest choice in degrees Celsius per minute. Choice B.

Question 1·SAT Desmos Regression Practice·Problem Solving and Data Analysis

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