Question

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.
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:
\[
y = 0.293x + 2.3
\]