Answer :
Certainly! Let's go through a detailed step-by-step process to solve the given questions regarding the relationship between the weight of candy bars and their calorie content:
(e) Predicting Calories for a Candy Bar Weighing 51.7 grams:
To predict the number of calories in a candy bar weighing 51.7 grams, we use the linear equation of the form:
[tex]\[ y = mx + b \][/tex]
Where:
- [tex]\( y \)[/tex] represents the number of calories.
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( x \)[/tex] is the weight of the candy bar in grams.
- [tex]\( b \)[/tex] is the y-intercept.
From the results:
- The slope [tex]\( m = 2.3333653718397422 \)[/tex]
- The y-intercept [tex]\( b = 213.97155743892313 \)[/tex]
Now, insert the weight [tex]\( x = 51.7 \)[/tex] grams into the equation:
[tex]\[ y = 2.3333653718397422 \times 51.7 + 213.97155743892313 \][/tex]
Calculate:
[tex]\[ y \approx 334.6065471630378 \][/tex]
So, the predicted number of calories for a candy bar weighing 51.7 grams is approximately 334.61 calories.
---
(f) Interpretation of the Slope:
The slope of the line, in this context, represents how the number of calories changes with respect to the change in weight of the candy bars.
In our linear equation, the slope is:
[tex]\[ m = 2.3333653718397422 \][/tex]
This number tells us that for every increase of 1 gram in the weight of a candy bar, the number of calories is expected to increase by 2.33 calories on average.
This information helps in understanding the relationship between the weight of a candy bar and its calorie content, indicating that they are directly proportional to each other.
(e) Predicting Calories for a Candy Bar Weighing 51.7 grams:
To predict the number of calories in a candy bar weighing 51.7 grams, we use the linear equation of the form:
[tex]\[ y = mx + b \][/tex]
Where:
- [tex]\( y \)[/tex] represents the number of calories.
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( x \)[/tex] is the weight of the candy bar in grams.
- [tex]\( b \)[/tex] is the y-intercept.
From the results:
- The slope [tex]\( m = 2.3333653718397422 \)[/tex]
- The y-intercept [tex]\( b = 213.97155743892313 \)[/tex]
Now, insert the weight [tex]\( x = 51.7 \)[/tex] grams into the equation:
[tex]\[ y = 2.3333653718397422 \times 51.7 + 213.97155743892313 \][/tex]
Calculate:
[tex]\[ y \approx 334.6065471630378 \][/tex]
So, the predicted number of calories for a candy bar weighing 51.7 grams is approximately 334.61 calories.
---
(f) Interpretation of the Slope:
The slope of the line, in this context, represents how the number of calories changes with respect to the change in weight of the candy bars.
In our linear equation, the slope is:
[tex]\[ m = 2.3333653718397422 \][/tex]
This number tells us that for every increase of 1 gram in the weight of a candy bar, the number of calories is expected to increase by 2.33 calories on average.
This information helps in understanding the relationship between the weight of a candy bar and its calorie content, indicating that they are directly proportional to each other.
