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The task asks to determine the equation of the line of best fit using linear regression based on the given data points. Here's how we approach the problem:

### Data Points:
- Time (min): [32, 36, 37, 39, 50]
- Mass (g): [48, 34, 31, 27, 24]

### Step-by-Step Process:
1. **Plot the Data**: The points are already plotted on the grid. They show a downward trend, suggesting that as time increases, the mass decreases.

2. **Calculate the Linear Regression**: We need to determine the equation of the line of best fit. The general form of the equation will be:
   \[
   y = mx + b
   \]
   where \(y\) is the mass, \(x\) is the time, \(m\) is the slope, and \(b\) is the y-intercept.

3. **Use of Linear Regression Formula**:
   The slope \(m\) and intercept \(b\) can be calculated using the least squares method, or you can input the data into a calculator or software that performs linear regression.

Let me calculate the slope \(m\) and the intercept \(b\) for you based on the given data.

I'll proceed with these calculations.The equation of the line of best fit, based on the linear regression performed on the data, is:

\[
y = -1.11x + 75.93
\]

Where:
- \(y\) is the mass in grams,
- \(x\) is the time in minutes,
- \(-1.11\) is the slope, and
- \(75.93\) is the y-intercept.

This equation shows that for every additional minute, the mass decreases by approximately 1.11 grams.

Would you like more details on any part of this process or further questions? Here are 5 related questions that might help:

1. How is the slope of the line of best fit interpreted in real-world terms?
2. How do I use a graphing calculator to perform linear regression?
3. What is the least squares method in linear regression?
4. How would the line of best fit change if the mass stayed constant over time?
5. Can we model other types of relationships, like exponential, with this data?

**Tip:** When using a graphing calculator or statistical software for regression, always check the residuals to ensure the model fits well.

Using your calculator, run a linear regression to determine the equation of the line of best fit. Round to two decimal places, use x for the variable.

Learn how to calculate the equation of the line of best fit using linear regression for a dataset involving time (in minutes) and mass (in grams). This problem covers linear regression, slope-intercept form, and least squares regression. Suitable for high school students in Grades 10-12.

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