Question

as people age, daily stress and worry decrease and happiness increases, according to an analysis of 340,847 adults ages 18 to 85 in a certain country. the graphs show a portion of the research. complete parts (a) and (b) below.
a. find the slope of the line passing through the two points shown in the line graph. express the slope as a decimal.
-0.4 (round to one decimal place as needed.)
b. use the answer from part (a) to complete the statement.
for each year of aging, the percentage of americans reporting \a lot\ of stress decreases by
% . the rate of change is
% per

Explanation:

Step1: Recall slope - rate of change relationship

The slope of the line represents the rate of change. In part (a), the slope of the line passing through the points $(22,46)$ and $(62,29)$ is calculated as $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{29 - 46}{62 - 22}=\frac{- 17}{40}=-0.425\approx - 0.4$.

Step2: Interpret the slope as a rate of change

The slope $m=-0.4$ means that for each unit increase in the $x$ - variable (age), the $y$ - variable (percentage of people reporting a lot of stress) changes by $-0.4$. So for each year of aging, the percentage of Americans reporting "a lot" of stress decreases by $0.4\%$. The rate of change is $-0.4\%$ per year.

Answer:

For each year of aging, the percentage of Americans reporting "a lot" of stress decreases by $0.4\%$. The rate of change is $-0.4\%$ per year.