Aging Reduces Stress and Increases Happiness

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Question:

s 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 bar graph with a horizontal axis with the labels 22 and 62 and a vertical axis labeled Percentage Reporting Stress from 0 to 60 in increments of 10 contains two vertical bars, where each bar is over a horizontal axis label. The heights of the bars are as follows, where the horizontal axis label is listed first and the height is listed second: 22, 49; 62, 27. 22 62 0 10 20 30 40 50 60 Percentage Reporting Stress Age 0 15 30 45 60 75 0 10 20 30 40 50 60 Age Percentage Reporting Stress (22,49) (62,27)

A coordinate plane has a horizontal x-axis labeled Age from 0 to 75 in increments of 15 and a vertical y-axis labeled Percentage Reporting Stress from 0 to 60 in increments of 10. A line segment falling from left to right has a left endpoint labeled (22, 49) and a right endpoint labeled (62, 27). Question content area bottom Part 1 a. Find the slope of the line passing through the two points shown in the line graph. Express the slope as a decimal.    enter your response here ​(Round to one decimal place as​ needed.) Part 2 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 ▼ negative 0.6 0.6 27 49 ​%. The rate of change is ▼ 0.6 49 27 negative 0.6 ​% per ▼ year of aging. age group. value of m. percentage of stress.

Answer:

To find the slope of the line passing through the two points (22, 49) and (62, 27), we can use the formula for the slope ( m ):

[ m = \frac{y_2 - y_1}{x_2 - x_1} ]

Where:

  • ( (x_1, y_1) = (22, 49) )
  • ( (x_2, y_2) = (62, 27) )

Substituting the values into the formula:

[ m = \frac{27 - 49}{62 - 22} = \frac{-22}{40} = -0.55 ]

Rounding to one decimal place, the slope is:

[ m \approx -0.6 ]

Part 1

a. The slope of the line is -0.6.

Part 2

b. For each year of aging, the percentage of Americans reporting "a lot" of stress decreases by negative 0.6%. The rate of change is negative 0.6% per year of aging.

So, the completed statement is:

For each year of aging, the percentage of Americans reporting "a lot" of stress decreases by negative 0.6%. The rate of change is negative 0.6% per year of aging.