The table lists how poverty level income cutoffs​ (in dollars) for a family of four have changed over time. Use the midpoint formula to approximate the poverty level cutoff in 1987 to the nearest dollar.
Year
Income​ (in dollars)
1970
3463
1980
8266
1990
13720
2000
17651
2004
19966
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Part 1
The poverty level cutoff in 1987 was 
  
enter your response here dollars.
​(Round to the nearest dollar as​ needed.)  

To approximate the poverty level cutoff for the year 1987 using the midpoint formula, we'll first identify the relevant data points. Since 1987 is between 1980 and 1990, we'll use the income values for those two years to calculate the midpoint.

The midpoint formula is given by:

\[
\text{Midpoint} = \frac{y_1 + y_2}{2}
\]

Where:
- $y_1$ is the income in 1980, which is 8266 dollars.
- $y_2$ is the income in 1990, which is 13720 dollars.

Substituting these values into the formula:

\[
\text{Midpoint} = \frac{8266 + 13720}{2} = \frac{21986}{2} = 10993
\]

Therefore, the poverty level cutoff in 1987 is approximately **10993 dollars**.

Would you like more details or have any questions?

Here are some related questions to explore:
1. How do income levels between 1970 and 2000 compare?
2. Can the poverty cutoff be modeled with linear interpolation over multiple decades?
3. What was the percentage increase in the poverty cutoff from 1980 to 1990?
4. How would a different year, like 1985, affect the midpoint formula calculation?
5. How does this poverty cutoff compare to the inflation rate during this period?

**Tip:** The midpoint formula is often used for estimating values between two known data points in linear trends.

The table lists how poverty level income cutoffs (in dollars) for a family of four have changed over time. Use the midpoint formula to approximate the poverty level cutoff in 1987 to the nearest dollar.
Year
Income (in dollars)
1970 - 3463
1980 - 8266
1990 - 13720
2000 - 17651
2004 - 19966
The poverty level cutoff in 1987 was ______ dollars. (Round to the nearest dollar as needed.)

This problem teaches you how to use the midpoint formula to estimate the poverty level income cutoff for a family of four in 1987, based on data from 1980 and 1990. Suitable for students in Grades 9-11, the solution uses linear estimation to find the income cutoff, with a final answer of approximately $10,993.

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