People who are severely obese ​(BMIgreater than or equals​40) are at most risk for serious health​ problems, which are the most expensive to treat. The percent of people in a country who are severely obese from 2000 and projected to 2030 is shown in the table.

Question

Year
2000
2010
2015
2020
2025
2030

​ % Severely Obese
2.3
4.8
6.5
7.8
9.3
11.1
Complete parts ​(a) through ​(c) below.
Question content area bottom
Part 1
a. Find the linear function that models severe​ obesity, with x equal to the number of years after 2000 and y equal to the percent of severe obesity in the country.
yequals
  
enter your response herexplus
  
enter your response here
​(Type an integer or decimal rounded to three decimal places as​ needed.)

Answer 1

To find the linear function that models severe obesity based on the provided data, we need to start by translating the years into "x" values, where \( x \) is the number of years after 2000:

• For 2000: \( x = 0 \), \( y = 2.3 \)
• For 2010: \( x = 10 \), \( y = 4.8 \)
• For 2015: \( x = 15 \), \( y = 6.5 \)
• For 2020: \( x = 20 \), \( y = 7.8 \)
• For 2025: \( x = 25 \), \( y = 9.3 \)
• For 2030: \( x = 30 \), \( y = 11.1 \)

Using two points for the linear function, let's take the points \( (0, 2.3) \) and \( (30, 11.1) \).

1. Find the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{11.1 - 2.3}{30 - 0} = \frac{8.8}{30} \approx 0.2933 \]

2. Use point-slope form to find the linear equation: \[ y - y_1 = m(x - x_1) \] Using the point \( (0, 2.3) \): \[ y - 2.3 = 0.2933(x - 0) \] \[ y = 0.2933x + 2.3 \]

So, the linear function that models severe obesity is:

\[ y = 0.293x + 2.3 \]

Final response:

• Enter response for the slope: 0.293 (rounded to three decimal places)
• Enter response for the y-intercept: 2.3

Thus, the linear function is: \[ y = 0.293x + 2.3 \]