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It looks like the text refers to a problem about linear regression or a similar concept, where the y-intercept and slope are explained in the context of running and burning calories.

From the image, the problem states:
- The **y-intercept** represents the number of calories a person burns per lap when running at a certain speed (given in mph).
- The **slope** represents the additional calories burned for each increase of 1 mph in speed.

The two blanks in the problem likely require the values for:
1. The number of calories burned per lap when running at a base speed (y-intercept).
2. The additional calories burned per lap for each mph increase in speed (slope).

To solve this, you typically need data points showing speed and corresponding calories burned. From that, you could use the linear regression formula \( y = mx + b \), where:
- \( y \) is the calories burned,
- \( m \) is the slope (calories burned per mph),
- \( x \) is the running speed in mph,
- \( b \) is the y-intercept (calories burned at 0 mph, typically just the base number).

Do you have additional data or problem statements related to this, such as the corresponding problem in the textbook (Problem 30) or given data points? This would help in calculating the exact values for the y-intercept and slope.

Would you like me to go through further details or guide you through how to calculate these values?

### Here are some related questions:
1. How do you calculate the slope in a linear equation based on given data points?
2. What does the y-intercept represent in real-world situations, especially for fitness-related data?
3. How can we apply linear regression techniques to model relationships between variables like speed and calories?
4. Can you explain why increasing speed by 1 mph affects calorie burn linearly in this model?
5. What assumptions are made when using a linear model in fitness or running scenarios?

**Tip:** Always check whether real-world data fits a linear model before applying a slope and y-intercept; sometimes the relationship may be non-linear!

This problem refers to problem 30 from the exercise set. Type your answers to the nearest hundredth. The y-intercept means that if a person runs at ____ mph they will burn ____ calories per lap. The slope means for each mph increase, you will burn an additional ____ calories per lap.

Solve a linear regression problem involving running speed and calories burned. This problem asks for the y-intercept and slope, key components of the equation y = mx + b. It covers important concepts in algebra and linear regression, suitable for high school students (Grades 9-12).

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