A line of best fit summarizes a roughly straight scatterplot rather than connecting every dot. Read widely separated points along the trend, then use Desmos to divide the temperature change by the altitude change for the slope. Read the temperature near zero altitude for the intercept. A line can match one part of the plot yet miss the overall pattern.
Hints
- Hint 1
The intercept is the temperature a line predicts when altitude is , because the term containing disappears. Look at the left edge of the scatterplot. About what temperature should a fitted line start at?
- Hint 2
The slope compares the change in temperature with the change in altitude. Choose points far apart across the downward trend; a short stretch between nearby dots may not represent the whole plot.
Step-by-step
Estimate from the scatterplot
Step 1Read across the trend
The dots near and are far apart and follow the roughly straight downward pattern. Read their coordinates using the labeled axes: altitude runs horizontally, and temperature runs vertically. Using the full span gives a better estimate of the trend than using two neighboring measurements.
- Step 2
Find the temperature change per altitude unit
The slope is the change in temperature divided by the change in altitude. Type in Desmos; it prints . So the trend is a drop of about degrees Fahrenheit for each additional thousand feet. The negative sign agrees with the downward pattern.
- Step 3
Match the starting temperature
In , the intercept is the predicted temperature when . The plot starts near degrees Fahrenheit, so use with the estimated slope: . A best-fit line follows the overall trend, not necessarily every dot. This equation is a reasonable model for temperature at the balloon’s altitude. Choice A.