When x=5, y=59.8
When x=15, y=67
When x=25, y=75
When x=35, y=88
When x=45, y=100

The data you've provided seems to represent a relationship between \( x \) and \( y \). To model this relationship, we can try fitting a linear or another type of function.

Let’s first check if the relationship between \( x \) and \( y \) is linear by calculating the slope between consecutive points:

1. Slope between \( (5, 59.8) \) and \( (15, 67) \):
   \[
   \text{slope} = \frac{67 - 59.8}{15 - 5} = \frac{7.2}{10} = 0.72
   \]

2. Slope between \( (15, 67) \) and \( (25, 75) \):
   \[
   \text{slope} = \frac{75 - 67}{25 - 15} = \frac{8}{10} = 0.8
   \]

3. Slope between \( (25, 75) \) and \( (35, 88) \):
   \[
   \text{slope} = \frac{88 - 75}{35 - 25} = \frac{13}{10} = 1.3
   \]

4. Slope between \( (35, 88) \) and \( (45, 100) \):
   \[
   \text{slope} = \frac{100 - 88}{45 - 35} = \frac{12}{10} = 1.2
   \]

The slopes vary, suggesting that the relationship between \( x \) and \( y \) may not be strictly linear. Instead, we might explore fitting a polynomial or other type of curve.

Would you like me to calculate a polynomial regression or investigate further patterns?

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### 5 Relative Questions:
1. Do you want to calculate a regression line (if it's assumed to be linear)?
2. Shall we fit a second-degree or higher polynomial to better match the data?
3. Are there additional data points, or is this the complete set?
4. Do you need to predict values for other \( x \)-values based on this data?
5. Would you like a graphical representation of the data?

**Tip**: When analyzing data, always check if the pattern is consistent with the assumed model (linear, quadratic, etc.) by comparing slopes or differences.

When x=5, y=59.8 When x=15, y=67 When x=25, y=75 When x=35, y=88 When x=45, y=100

Explore the relationship between x and y values, including data points like (5, 59.8), (15, 67), (25, 75), (35, 88), and (45, 100). Learn how to calculate slopes, assess linearity, and fit polynomial models to find patterns. This analysis is suitable for students in Grades 9-12.

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