Question 3·Hard·Two-Variable Data: Models and Scatterplots
The scatterplot below displays the mean daily temperature and the number of ice-cream cones sold at a beach stand for eight randomly selected days. A line of best fit for the data is also shown.
According to the line of best fit, which of the following is closest to the predicted number of ice-cream cones the stand would sell on a day when the mean temperature is ?
For scatterplot questions with a line of best fit, always work from the given model (the line) rather than from individual dots. Quickly locate the given -value on the horizontal axis, move up or down to the line, then move sideways to the vertical axis to read an approximate -value. Don’t worry about being exact—just estimate carefully and then choose the closest answer choice, keeping an eye out for choices that reflect common over- or under-estimates of your visual reading.
Hints
Use the line, not the dots
The question specifically mentions the line of best fit. Focus on that straight line rather than any individual data point when making your prediction.
Start from the temperature value
Find 23 on the horizontal axis (mean temperature). From that point, move straight up until you reach the line of best fit.
Then read across to the cones axis
Once you hit the line of best fit at , move horizontally to the axis labeled with the number of cones sold and estimate that value. Then pick the answer choice that is closest to your estimate.
Desmos Guide
Approximate an equation for the line of best fit
From the graph, visually pick two clear points that lie exactly on the line of best fit, say and where both coordinates hit grid intersections. In Desmos, compute the slope using , then write an equation like y = m x + b that goes through one of the points.
Use your line equation to find the prediction at 23°C
Once you have your line’s equation in Desmos (for example, typed as y = m x + b with your actual numbers), type a new expression y(23) or substitute x = 23 into the equation. The output -value is the predicted number of cones sold at . Compare that value to the answer choices and select the closest one.
Step-by-step Explanation
Understand what the question is asking
The scatterplot shows individual days, but the question says "According to the line of best fit". That means you should ignore the individual data points and instead use the straight line drawn through the middle of the data.
You are predicting the number of cones sold (vertical axis) when the temperature is (horizontal axis).
Locate 23°C on the horizontal axis
On the temperature (horizontal) axis, find the tick mark labeled 23 (or the place between 22 and 24 that corresponds to 23).
From that point on the horizontal axis, imagine or draw a light vertical line upward until it touches the line of best fit (not a dot). The intersection point shows the model’s predicted number of cones for .
Read the corresponding value on the vertical axis
From the intersection point on the line of best fit, move horizontally to the left or right to the vertical axis that shows number of cones sold.
Read off the approximate -value there. It should fall between two labeled grid lines; estimate it based on spacing (for example, if the intersection is halfway between 180 and 220, use the midpoint between those labels).
Match your estimate to the closest answer choice
Compare your estimated -value from the vertical axis with the answer choices: 180, 190, 200, and 220.
The line at is closest to 200 cones, so the best answer is 200.