Question

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. the poverty level cutoff in 1987 was dollars. (round to the nearest dollar as needed.)

Explanation:

Step1: Identify the relevant years

We use the data for 1980 ($x_1 = 1980$, $y_1=8109$) and 1990 ($x_2 = 1990$, $y_2 = 13115$) since 1987 is between 1980 and 1990.

Step2: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

$$ m=\frac{13115 - 8109}{1990 - 1980}=\frac{5006}{10}=500.6 $$

Step3: Use the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(x_1,y_1)=(1980,8109)$ and $x = 1987$.

$$ y-8109=500.6\times(1987 - 1980) $$

$$ y-8109=500.6\times7 $$

$$ y-8109 = 3504.2 $$

$$ y=8109+3504.2=11613.2 $$

Answer:

11613