To find the equation for the line of best fit representing a woman's height, [tex]\( y \)[/tex], based on her shoe size, [tex]\( x \)[/tex], let's proceed step by step.
Given a data set containing shoe sizes and corresponding heights, we aim to find a linear relationship between these variables. In a linear equation of the form [tex]\( y = mx + b \)[/tex]:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept of the line.
### Step 1: Input the Data Points
The given data points are:
- [tex]\( (7.5, 63) \)[/tex]
- [tex]\( (9, 72.5) \)[/tex]
- [tex]\( (11, 70) \)[/tex]
- [tex]\( (7, 62) \)[/tex]
- [tex]\( (9, 69.5) \)[/tex]
- [tex]\( (10, 72) \)[/tex]
- [tex]\( (12, 72.5) \)[/tex]
- [tex]\( (13, 73) \)[/tex]
- [tex]\( (13, 70) \)[/tex]
### Step 2: Best Fit Line Calculation
The best fit line can be computed using the least squares method for linear regression, where the slope [tex]\( m \)[/tex] and y-intercept [tex]\( b \)[/tex] are determined.
From our calculated result:
- [tex]\( \text{slope, } m = 1.3604 \)[/tex]
- [tex]\( \text{intercept, } b = 55.558 \)[/tex]
### Step 3: Formulating the Equation
Using the calculated slope and intercept, we can write the linear equation as:
[tex]\[ y = 1.3604x + 55.558 \][/tex]
With some slight rounding and comparison to the given options, the equation is closest to the form:
[tex]\[ y = 1.36x + 55.6 \][/tex]
Thus, the correct equation for the line of best fit for a woman's height [tex]\( y \)[/tex], based on her shoe size [tex]\( x \)[/tex], is:
[tex]\[ y = 1.36x + 55.6 \][/tex]
### Conclusion
The correct answer is:
[tex]\[ y = 1.36x + 55.6 \][/tex]
Therefore, among the given options, the answer is:
[tex]\[ \boxed{y = 1.36x + 55.6} \][/tex]
