# Math Help - Linear Equations in Two Variables

1. ## Linear Equations in Two Variables

I am having some trouble with this problem and would greatly appreciate it if someone could help me out by solving it. Thanks!

Suppose you are told that the enrollment at the University of Florida was 36531 in 1990 and 48673 in 2003.

a. Assuming the enrollment growth is linear, find a linear model/equation that gives the enrollment in terms of t, where t=0 to the year 1900 (not a typo). Let E(t) denote the enrollment in year t. So I am looking for a linear equation in the two variables, t and E(t).

2. Hello, js0810!

The enrollment at the University of Florida was 36,531 in 1990 and 48,673 in 2003.

a. Assuming the enrollment growth is linear, find a linear model/equation
that gives the enrollment in terms of t, where t=0 to the year 1900 (not a typo).

Let $E(t)$ denote the enrollment in year $t$.

Since $t = 0$ represents the year 1900,
. . then $t$ is the number of years after 1900.

We are given two points: . $\begin{array}{|c|c|c|} t & E(t) & (t,E)\\ \hline \hline
90 & 36,\!531 & (90,\,36,\!531)\\ \hline 103 & 48,\!673 & (103,\,48,\!673) \\ \hline \end{array}$

And we want the equation of the line through these two points.

The slope is: . $m \:=\:\frac{48,\!673-36,\!531}{103-90} \:=\:\frac{12,\!142}{13} \:=\:934$

The equation of the line through (90, 35,531) and slope 934 is:

. . $E - 36,\!531 \;=\;934(t - 90) \quad\Rightarrow\quad\boxed{ E \;=\;934t - 47,\!529}$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

An amusing thought struck me . . . That's a strange function.

It says: in the year 1900, there were -47,529 students enrolled.
Not only were there no students, there were over 47 thousand
. . who were actively opposed to attending UofF.
. .
(probably picketing outside the campus gate)

Over the years the number of protesters gradually diminished
. . until in 1950, there were only 829 of them.

Then in 1951, the first 105 students enrolled . . .

3. Thanks for the help everyone!