Question 41·Medium·Two-Variable Data: Models and Scatterplots
The scatterplot shown represents the relationship between simmering time (in minutes) and soup temperature (in degrees Celsius). A line of best fit for the data is also shown.
Based on the line of best fit, when the simmering time increases from minutes to minutes, by approximately how many degrees Celsius does the soup temperature increase?
When a question asks for an increase over an interval using a line of best fit, find the slope from two clear points on the line, then multiply the slope by the change in (here, ).
Hints
Use the line of best fit
Read points from the line of best fit (not individual scattered points) to estimate the overall trend.
Compute the slope
Pick two grid-intersection points on the line and compute .
Turn slope into the requested change
The question asks for the increase from to , so multiply the slope by .
Desmos Guide
Enter two points from the line
From the graph, use the two points on the best-fit line: and .
Graph the line through those points
In Desmos, enter
y-14=((34-14)/(10-2))*(x-2)
to graph the line of best fit.
Find the change from to
Evaluate the line at and (for example, by clicking points on the line at those -values), then subtract: (value at ) minus (value at ). Choose the closest answer choice.
Step-by-step Explanation
Find the slope from two points on the line
From the graph, the line of best fit passes through and . The slope is
So the temperature increases by about degrees Celsius per minute.
Find the change in time
From to , the time increases by minutes.
Compute the predicted increase and choose the closest option
Multiply the slope by the time change:
So the soup temperature increases by approximately degrees Celsius. The correct choice is 15.