Question

30 POINTS. Fake answers will be reported.

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In this activity, you will solve the problem presented in the introduction. Patricia wants to estimate the future consumer price index (CPI). She first found the CPI for January of every year from 1990 to 2010. She created a scatter plot of the data and drew the line of best fit as shown.

Part A
What is the equation for the line of best fit?

Part B
What would the x-value be to find the CPI for the year 2030?

Part C
Use the equation of the line of best fit and the value of x found for the year 2030 to estimate the CPI for the year 2030.

Answer 1

It’s 8 for part a it’s graphed to the right for part b and it’s 2000 for the average

Answer 2

Patricia estimated the future CPI using a scatter plot. The line of best fit's equation is y = 5x + 120. For the year 2030, the x-value is 382, and the estimated CPI is 2030.

To address the three parts of the problem:

Part A: Equation for the Line of Best Fit

The equation for the line of best fit is typically written in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

Given the points (0,120) and (20,220), we can find the slope (m):

`\[ m = \frac{\text{change in } y}{\text{change in } x} = (220 - 120)/(20 - 0) = (100)/(20) = 5 \]`

Now, we can use the slope and one of the points (e.g., (0,120)) to find the y-intercept (b):

`\[ b = y - mx = 120 - 5 * 0 = 120 \]`

So, the equation for the line of best fit is y = 5x + 120.

Part B: X-Value for the Year 2030

To find the x-value for the year 2030, we need to substitute the year (2030) into the equation and solve for x:

2030 = 5x + 120

5x = 2030 - 120

5x = 1910

`\[ x = (1910)/(5) = 382 \]`

Part C: Estimate CPI for the Year 2030

Now that we have the x-value (382) for the year 2030, we can use it in the equation:

y = 5x + 120

`\[ \text{CPI}_(2030) = 5 * 382 + 120 \]`

`\[ \text{CPI}_(2030) = 1910 + 120 \]`

`\[ \text{CPI}_(2030) = 2030 \]`

Therefore, the estimated CPI for the year 2030 is 2030.