Math Problem Statement

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. Based on the line of best fit, what temperature would it most likely be outside if this same species of cricket were measured to chirp 96 times in one minute?

Solution

The scatter plot in the image shows the relationship between the number of chirps per minute (x-axis) and the temperature (y-axis) for a certain species of cricket. The line of best fit is drawn, and you are asked to predict the temperature when the cricket chirps 96 times in one minute.

To solve this, we need to first derive the equation of the line of best fit from the scatter plot. From the points on the line, we can extract the slope (m) and the y-intercept (b). The equation of the line will be in the form of:

y=mx+by = mx + b

Where:

  • yy represents the temperature (dependent variable),
  • xx represents the chirps per minute (independent variable),
  • mm is the slope, and
  • bb is the y-intercept.

By finding the slope and y-intercept from the graph or the given points, we can substitute x=96x = 96 into the equation to find the corresponding temperature.

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Math Problem Analysis

Mathematical Concepts

Linear Relationships
Scatter Plots
Line of Best Fit
Linear Regression

Formulas

y = mx + b

Theorems

Slope-Intercept Form
Prediction Using a Line of Best Fit

Suitable Grade Level

Grades 7-9