Question

a researcher studied the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside. her data is expressed in the scatter plot and line of best fit below. what does the slope of the line represent?
scatter plot with x - axis labeled chirps per minute and y - axis labeled temperature (degrees fahrenheit)
answer options:

• how long the cricket continues to chirp
• the expected change in temperature in degrees fahrenheit for each additional cricket chirp in one minute
• the expected change in number of cricket chirps in one minute for each additional degree fahrenheit
• the expected temperature when the cricket chirps 1 time

Explanation:

To determine what the slope of the line of best fit represents, we analyze the variables: the x - axis is "Chirps Per Minute" (number of cricket chirps) and the y - axis is "Temperature (Degrees Fahrenheit)". The slope of a line in a scatter plot with a line of best fit is calculated as $\frac{\text{Change in }y}{\text{Change in }x}$. Here, the change in $y$ is the change in temperature (in degrees Fahrenheit) and the change in $x$ is the change in the number of cricket chirps per minute. So, the slope represents the expected change in the y - variable (temperature) for each unit change in the x - variable (number of cricket chirps per minute).

Let's analyze each option:

• "How long the cricket continues to chirp": The slope has nothing to do with the duration of chirping, so this is incorrect.
• "The expected change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute": This matches our analysis of the slope (change in y over change in x, where y is temperature and x is chirps per minute), so this is correct.
• "The expected change in number of cricket chirps in one minute for each additional degree Fahrenheit": This would be the reciprocal of the slope (change in x over change in y), which is not what the slope represents, so this is incorrect.
• "The expected temperature when the cricket chirps 1 time": This would be the y - intercept (the value of y when x = 0), not the slope, so this is incorrect.

Answer:

The expected change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.