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:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
The slope of a line can be found using this formula:
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]Where these two points are on the line:
[tex](x_1,y_1),(x_2,y_2)[/tex]In this case, you know these two points:
[tex](1,8.2),(5,17.4)[/tex]Then, you can substitute values into the formula and find the slope of the line:
[tex]m=\frac{17.4-8.2}{5-1}=\frac{9.2}{4}=2.3[/tex]Now you know that the form of the equation is:
[tex]n=2.3t+b[/tex]In order to find "b", you need to:
- Choose one of the points on the line:
[tex]\mleft(1,8.2\mright)[/tex]- Identify the value of each variable. Notice that:
[tex]\begin{gathered} n=8.2 \\ t=2001 \end{gathered}[/tex]- Substitute those values of "n" and "t", and the slope into the equation:
[tex]8.2=2.3(1)+b[/tex]- Solve for "b":
[tex]\begin{gathered} 8.2=2.3+b \\ 8.2-2.3=b \\ b=5.9 \end{gathered}[/tex]Therefore the equation of the Linear Model is:
[tex]n=2.3t+5.9[/tex]Hence, the answer is: Option D.
