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Answer :
To apply the median-fit method, we use three summary points:
- Extreme points:
[tex]$$ (x_1,y_1)=(45,425) \quad \text{and} \quad (x_3,y_3)=(97,915) $$[/tex]
- Median point:
[tex]$$ (x_2,y_2)=(62,651) $$[/tex]
Step 1. Calculate the slope.
Using the extreme points, the slope [tex]$m$[/tex] is given by:
[tex]$$
m = \frac{y_3 - y_1}{x_3 - x_1} = \frac{915 - 425}{97 - 45} = \frac{490}{52} \approx 9.4231.
$$[/tex]
Step 2. Calculate the [tex]$y$[/tex]-intercept.
With the median point [tex]$(62,651)$[/tex] and the slope found, the [tex]$y$[/tex]-intercept [tex]$b$[/tex] is calculated by:
[tex]$$
b = y_2 - m \cdot x_2 = 651 - (9.4231 \times 62) \approx 651 - 584.230 \approx 66.7692.
$$[/tex]
Step 3. Write the linear model.
Thus, the equation of the line of best fit (rounded to two decimal places) is:
[tex]$$
y = 9.42x + 66.77.
$$[/tex]
This is the linear model representing the caterer's data.
- Extreme points:
[tex]$$ (x_1,y_1)=(45,425) \quad \text{and} \quad (x_3,y_3)=(97,915) $$[/tex]
- Median point:
[tex]$$ (x_2,y_2)=(62,651) $$[/tex]
Step 1. Calculate the slope.
Using the extreme points, the slope [tex]$m$[/tex] is given by:
[tex]$$
m = \frac{y_3 - y_1}{x_3 - x_1} = \frac{915 - 425}{97 - 45} = \frac{490}{52} \approx 9.4231.
$$[/tex]
Step 2. Calculate the [tex]$y$[/tex]-intercept.
With the median point [tex]$(62,651)$[/tex] and the slope found, the [tex]$y$[/tex]-intercept [tex]$b$[/tex] is calculated by:
[tex]$$
b = y_2 - m \cdot x_2 = 651 - (9.4231 \times 62) \approx 651 - 584.230 \approx 66.7692.
$$[/tex]
Step 3. Write the linear model.
Thus, the equation of the line of best fit (rounded to two decimal places) is:
[tex]$$
y = 9.42x + 66.77.
$$[/tex]
This is the linear model representing the caterer's data.
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