Question

A new high school math project is being tested in the state. In the first year (year 1), there are students involved. By the end of the third year (year 3), students are expected to be involved. Assuming the increase is linear, write the equation of the line, in slope-intercept form, representing the number of students participating in this project for each year x. Use this result to predict the number of students involved at the end of 5 years.Hint: Use the ordered pairs (1, ) and (3, ).

Answer 1

Solution

Let y be the number of students involved.

let x be the years.

when

x = 1, y = 603

x = 3, y = 12545

Since the increase is linear,

$\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \\ \Rightarrow\frac{y-603}{x-1}=\frac{12545-603}{3-1} \\ \\ \Rightarrow\frac{y-603}{x-1}=\frac{11942}{2} \\ \\ \Rightarrow\frac{y-603}{x-1}=5971 \\ \\ \Rightarrow y-603=(x-1)\times5971 \\ \\ \Rightarrow y-603=5971x-5971 \\ \\ \Rightarrow y=5971x-5971+603 \\ \\ \Rightarrow y=5971x-5368 \end{gathered}$

At the end of 5 years,

That is, when x = 5

$y=5971(5)-5368=24487$