Answered

Cherie measures and records the lengths and sizes of the same style of a sandal found at a shoe store.

| Foot length (in.) (x) | Shoe size (S) |
|-----------------------|---------------|
| 8 | 6 |
| 8.5 | 7 |
| 9 | 8 |
| 9.5 | 9 |
| 10 | 10 |

Which equation can be used to determine the approximate shoe size, [tex]\( S \)[/tex], for a foot length of [tex]\( x \)[/tex] inches?

A. [tex]\( S = x - 2 \)[/tex]
B. [tex]\( S = 2x - 10 \)[/tex]
C. [tex]\( S = x + 6 \)[/tex]
D. [tex]\( S = 2x + 4 \)[/tex]



Answer :

GinnyAnswer
To determine the equation that relates foot length ([tex]\( x \)[/tex]) to shoe size ([tex]\( S \)[/tex]), we can perform linear regression to find the best-fit line for the given data points.

Given data:
[tex]\[ \begin{array}{|c|c|} \hline \text{Foot length (in.)} \; (x) & \text{Shoe size} \; (S) \\ \hline 8 & 6 \\ \hline 8.5 & 7 \\ \hline 9 & 8 \\ \hline 9.5 & 9 \\ \hline 10 & 10 \\ \hline \end{array} \][/tex]

With linear regression, we look for a linear equation of the form [tex]\( S = mx + c \)[/tex] where [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] is the y-intercept.

After performing the necessary calculations:

1. Calculate the Slope ([tex]\( m \)[/tex]):
- The slope [tex]\( m = 2 \)[/tex].

2. Calculate the Intercept ([tex]\( c \)[/tex]):
- The intercept [tex]\( c = -10 \)[/tex].

Thus, the equation derived from the linear regression analysis is:
[tex]\[ S = 2x - 10 \][/tex]

Therefore, the correct equation to determine the approximate shoe size ([tex]\( S \)[/tex]) for a foot length ([tex]\( x \)[/tex]) is:
[tex]\[ S = 2x - 10 \][/tex]

So the correct answer is:
[tex]\[ \boxed{S = 2x - 10} \][/tex]

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