Answer :
To find the equation that best fits the given data relating foot length [tex]\(x\)[/tex] to shoe size [tex]\(S\)[/tex], we need to check which provided formula correctly represents the relationship between these two variables for all given data points.
The data provided are:
- When [tex]\( x = 8 \)[/tex], [tex]\( S = 6 \)[/tex]
- When [tex]\( x = 8.5 \)[/tex], [tex]\( S = 7 \)[/tex]
- When [tex]\( x = 9 \)[/tex], [tex]\( S = 8 \)[/tex]
- When [tex]\( x = 9.5 \)[/tex], [tex]\( S = 9 \)[/tex]
- When [tex]\( x = 10 \)[/tex], [tex]\( S = 10 \)[/tex]
Let's check each equation one by one:
1. [tex]\( S = x - 2 \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( S = 8 - 2 = 6 \)[/tex] (matches)
- For [tex]\( x = 8.5 \)[/tex]: [tex]\( S = 8.5 - 2 = 6.5 \)[/tex] (does not match)
- Therefore, [tex]\( S = x - 2 \)[/tex] does not fit all data points.
2. [tex]\( S = 2x - 10 \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( S = 2(8) - 10 = 16 - 10 = 6 \)[/tex] (matches)
- For [tex]\( x = 8.5 \)[/tex]: [tex]\( S = 2(8.5) - 10 = 17 - 10 = 7 \)[/tex] (matches)
- For [tex]\( x = 9 \)[/tex]: [tex]\( S = 2(9) - 10 = 18 - 10 = 8 \)[/tex] (matches)
- For [tex]\( x = 9.5 \)[/tex]: [tex]\( S = 2(9.5) - 10 = 19 - 10 = 9 \)[/tex] (matches)
- For [tex]\( x = 10 \)[/tex]: [tex]\( S = 2(10) - 10 = 20 - 10 = 10 \)[/tex] (matches)
- Therefore, [tex]\( S = 2x - 10 \)[/tex] fits all data points.
3. [tex]\( S = x + 6 \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( S = 8 + 6 = 14 \)[/tex] (does not match)
- Therefore, [tex]\( S = x + 6 \)[/tex] does not fit all data points.
4. [tex]\( S = 2x + 4 \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( S = 2(8) + 4 = 16 + 4 = 20 \)[/tex] (does not match)
- Therefore, [tex]\( S = 2x + 4 \)[/tex] does not fit all data points.
After evaluating all the equations, we find that the equation [tex]\( S = 2x - 10 \)[/tex] is the only one that correctly fits all the provided data points. Therefore, the equation that can be used to determine the approximate shoe size [tex]\( S \)[/tex] for a foot length [tex]\( x \)[/tex] inches is:
[tex]\[ S = 2x - 10 \][/tex]
The data provided are:
- When [tex]\( x = 8 \)[/tex], [tex]\( S = 6 \)[/tex]
- When [tex]\( x = 8.5 \)[/tex], [tex]\( S = 7 \)[/tex]
- When [tex]\( x = 9 \)[/tex], [tex]\( S = 8 \)[/tex]
- When [tex]\( x = 9.5 \)[/tex], [tex]\( S = 9 \)[/tex]
- When [tex]\( x = 10 \)[/tex], [tex]\( S = 10 \)[/tex]
Let's check each equation one by one:
1. [tex]\( S = x - 2 \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( S = 8 - 2 = 6 \)[/tex] (matches)
- For [tex]\( x = 8.5 \)[/tex]: [tex]\( S = 8.5 - 2 = 6.5 \)[/tex] (does not match)
- Therefore, [tex]\( S = x - 2 \)[/tex] does not fit all data points.
2. [tex]\( S = 2x - 10 \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( S = 2(8) - 10 = 16 - 10 = 6 \)[/tex] (matches)
- For [tex]\( x = 8.5 \)[/tex]: [tex]\( S = 2(8.5) - 10 = 17 - 10 = 7 \)[/tex] (matches)
- For [tex]\( x = 9 \)[/tex]: [tex]\( S = 2(9) - 10 = 18 - 10 = 8 \)[/tex] (matches)
- For [tex]\( x = 9.5 \)[/tex]: [tex]\( S = 2(9.5) - 10 = 19 - 10 = 9 \)[/tex] (matches)
- For [tex]\( x = 10 \)[/tex]: [tex]\( S = 2(10) - 10 = 20 - 10 = 10 \)[/tex] (matches)
- Therefore, [tex]\( S = 2x - 10 \)[/tex] fits all data points.
3. [tex]\( S = x + 6 \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( S = 8 + 6 = 14 \)[/tex] (does not match)
- Therefore, [tex]\( S = x + 6 \)[/tex] does not fit all data points.
4. [tex]\( S = 2x + 4 \)[/tex]
- For [tex]\( x = 8 \)[/tex]: [tex]\( S = 2(8) + 4 = 16 + 4 = 20 \)[/tex] (does not match)
- Therefore, [tex]\( S = 2x + 4 \)[/tex] does not fit all data points.
After evaluating all the equations, we find that the equation [tex]\( S = 2x - 10 \)[/tex] is the only one that correctly fits all the provided data points. Therefore, the equation that can be used to determine the approximate shoe size [tex]\( S \)[/tex] for a foot length [tex]\( x \)[/tex] inches is:
[tex]\[ S = 2x - 10 \][/tex]
