In 19981998​, the percentage of​ 18- to​ 29-year-olds who used the Internet was 7171​%. In 20072007​, that percentage had risen to 8787​%. Complete parts​ (a) through​ (d) below.
Question content area bottom
Part 1
​a) Use the year as the​ x-coordinate and the percentage as the​ y-coordinate. Find the equation of the line that contains the data points.
yequals=StartFraction 16 Over 9 EndFraction x minus 3481
16
9x−3481
​(Type an exact answer. Do not include the​ % symbol in your​ answer.)
Part 2
​b) Use the equation in part​ (a) to estimate the percentage of Internet users in 20122012.
The percentage of Internet users in 20122012 is approximately enter your response here​%.
​(Simplify your answer. Use the answer from part​ (a) to find this answer. Round to the nearest tenth as needed. Do not include the​ % symbol in your​ answer.)

### Part 1:
**a) Finding the equation of the line:**

To find the equation of the line, we will use the two points given, corresponding to the years and percentages:  
\( (1998, 71) \) and \( (2007, 87) \).

The slope \( m \) of the line is calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{87 - 71}{2007 - 1998} = \frac{16}{9}
\]

Now, using the point-slope form of the equation of a line:
\[
y - y_1 = m(x - x_1)
\]
Substitute \( m = \frac{16}{9} \) and the point \( (1998, 71) \):
\[
y - 71 = \frac{16}{9}(x - 1998)
\]

Now, solve for \( y \):
\[
y = \frac{16}{9}(x - 1998) + 71
\]

Distribute the \( \frac{16}{9} \):
\[
y = \frac{16}{9}x - \frac{16}{9} \times 1998 + 71
\]
\[
y = \frac{16}{9}x - 3555.11 + 71
\]
\[
y = \frac{16}{9}x - 3484.11
\]

Thus, the equation of the line is approximately:
\[
y = \frac{16}{9}x - 3484.11
\]

### Part 2:
**b) Estimating the percentage of Internet users in 2012:**

Now, use the equation \( y = \frac{16}{9}x - 3484.11 \) and substitute \( x = 2012 \) to estimate the percentage for 2012.

\[
y = \frac{16}{9} \times 2012 - 3484.11
\]
Let me calculate this.The estimated percentage of Internet users in 2012 is approximately \( 92.8\% \).

Would you like any further clarification or more details?

Here are 5 related questions:
1. How do you calculate the slope of a line between two points?
2. What is the point-slope form of a linear equation?
3. How do you interpret the y-intercept in this context?
4. How can linear interpolation or extrapolation be used in real-world predictions?
5. What assumptions are made when predicting future percentages based on past data?

**Tip:** When solving for a line equation from data points, always verify whether the equation makes sense by substituting values to check consistency.

In 1998, the percentage of​ 18- to​ 29-year-olds who used the Internet was 71%. In 2007, that percentage had risen to 87%. Complete parts​ (a) through​ (d) below. a) Use the year as the​ x-coordinate and the percentage as the​ y-coordinate. Find the equation of the line that contains the data points. y = (16/9)x - 3481 b) Use the equation in part​ (a) to estimate the percentage of Internet users in 2012.

Learn how to find the equation of a line using data points for Internet usage among 18-29-year-olds from 1998 to 2007. This problem involves calculating the slope and applying the slope-intercept form to predict future percentages. Ideal for students in Grades 9-12.

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