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Problem-Solving and Data Analysis / Two-variable data: Models and scatterplots Difficulty: Hard

The figure presents a scatterplot titled “Number of Beach Visitors versus Temperature.” The horizontal axis is labeled “Average temperature, in degrees Celsius,” and the numbers 25 through 35, in increments of 2, are indicated. The vertical axis is labeled “Number of people,” and the numbers 0 through 640, in increments of 80, are indicated. There are 11 data points in the scatterplot that begin near the bottom left portion of the coordinate plane and trend upward and to the right. The line of best fit for the data is also shown. The line of best fit passes through the points with coordinates 25 comma 80 and 32 comma 480.


Each dot in the scatterplot above represents the temperature and the number of people who visited a beach in Lagos, Nigeria, on one of eleven different days. The line of best fit for the data is also shown. The line of best fit for the data has a slope of approximately 57. According to this estimate, how many additional people per day are predicted to visit the beach for each 5°C increase in average temperature?

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Explanation

The correct answer is 285. The number of people predicted to visit the beach each day is represented by the y-values of the line of best fit, and the average temperature, in degrees Celsius (degrees Celsius), is represented by the x-values. Since the slope of the line of best fit is approximately 57, the y-value, or the number of people predicted to visit the beach each day, increases by 57 for every x-value increase of 1, or every 1 degree Celsius increase in average temperature. Therefore, an increase of 5 degrees Celsius in average temperature corresponds to a y-value increase of 57 times 5, equals 285 additional people per day predicted to visit the beach.