Question

The number of classified documents has increased approximately linear from 8.2 million documents in 2001 to 17. 4 million documents in 2005. let in be the number of documents in millions labeled as classified in the year that is years since 2000 find the equation of the linear model to describe the data

Answer 1

Knowing that

- The number of classified documents has increased linearly.

- In 2001 there were 8.2 million documents.

- In 2005 there were 17.4 million documents.

- The variable "n" represents the number of documents (in millions) labeled as classified.

- The variable "t" represents the number of years since 2000.

The Slope-Intercept Form of the equation of a line is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

The slope of a line can be found using this formula:

`m=\frac{y_2-y_1_{}}{x_2-x_1}`

Where these two points are on the line:

`(x_1,y_1),(x_2,y_2)`

In this case, you know these two points:

`(1,8.2),(5,17.4)`

Then, you can substitute values into the formula and find the slope of the line:

`m=(17.4-8.2)/(5-1)=(9.2)/(4)=2.3`

Now you know that the form of the equation is:

`n=2.3t+b`

In order to find "b", you need to:

- Choose one of the points on the line:

`\mleft(1,8.2\mright)`

- Identify the value of each variable. Notice that:

`\begin{gathered} n=8.2 \\ t=2001 \end{gathered}`

- Substitute those values of "n" and "t", and the slope into the equation:

`8.2=2.3(1)+b`

- Solve for "b":

`\begin{gathered} 8.2=2.3+b \\ 8.2-2.3=b \\ b=5.9 \end{gathered}`

Therefore the equation of the Linear Model is:

`n=2.3t+5.9`

Hence, the answer is: Option D.