The scatterplot shows the monthly high temperatures of Austin, Texas, in degrees Fahrenheit over a 12-month period.

Which function best models the data from Month 1 to Month 9?
A.y= —1.6x + 111
B.y= 3.5x + 85
C.y= 2.5x + 90
D.y= —3.3x + 130

To determine which function best models the data for Austin's monthly high temperatures from Month 1 to Month 9, we should consider the trends these linear equations represent. Here’s a step-by-step approach:

1. **Analyze the slope**:
   - Each function has a different slope (coefficient of \( x \)), which indicates how much the temperature changes per month.
     - \( A: -1.6 \) (slight decrease)
     - \( B: 3.5 \) (increase)
     - \( C: 2.5 \) (increase)
     - \( D: -3.3 \) (more significant decrease)

2. **Identify the overall trend from the scatterplot**:
   - If temperatures increase from Month 1 to Month 9, options B or C with positive slopes would be better choices.
   - If temperatures decrease, options A or D would be more suitable.

3. **Examine the intercept**:
   - The intercept values give a starting point at Month 1:
     - \( A: 111 \)
     - \( B: 85 \)
     - \( C: 90 \)
     - \( D: 130 \)

   Each equation's intercept might align with January's temperature. Choose the equation with an intercept closest to the observed value on the scatterplot.

If the trend shows a rising temperature (typical for winter to summer months), **Option B** with a slope of \( 3.5 \) and intercept \( 85 \) would likely be the best fit. 

Would you like further details, or do you have any questions about this analysis?

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1. How do we calculate the best-fit line for a scatterplot in general?
2. What does each part of a linear equation \( y = mx + b \) represent in terms of data modeling?
3. How would the choice change if data extended beyond Month 9?
4. What are the limitations of using a linear model for temperature data?
5. How would a quadratic model differ from a linear model in this context?

**Tip:** When looking at trends, start with the slope to quickly gauge if the data is increasing or decreasing.

The scatterplot shows the monthly high temperatures of Austin, Texas, in degrees Fahrenheit over a 12-month period. Which function best models the data from Month 1 to Month 9? A.y= —1.6x + 111 B.y= 3.5x + 85 C.y= 2.5x + 90 D.y= —3.3x + 130

Learn how to find the best linear function to model Austin's monthly high temperatures from Month 1 to Month 9. This example explores scatterplots, linear equations, and identifying the slope and intercept in real-world data. Suitable for students in Grades 8-10.

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