Answer
$y=181.5t+226.5$
Work Step by Step
Let $y$ be the number of teenagers who underwent gastric bypass surgery and $t$ be the number of years since $2000$. A linear equation for the number of teenagers having gastric bypass surgery $t$ years since $2000$ takes the form of
$$
y=mt+b,
$$
where $m$ is the slope and $b$ is the $y$-intercept.
Since in $2001$ (i.e. $1$ year since $2000$) the number of teenagers who underwent gastric bypass surgery is $408$, this can be represented by the ordered pair $(t_1,y_1)=(1,408)$. Since in $2003$ (i.e. $3$ years since $2000$) the number of teenagers who underwent gastric bypass surgery is $771$, this can be represented by the ordered pair $(t_2,y_2)=(3,771)$.
The formula for finding the slope, $m$, of the line passing through two points, $(t_1,y_1)$ and $(t_2,y_2)$ is given by $m=\frac{y_1-y_2}{t_1-t_2}$. That is,
$$\begin{aligned}
m&=\frac{y_1-y_2}{t_1-t_2}
\\&=
\frac{408-771}{1-3}
\\&=
\frac{-363}{-2}
\\&=
181.5
.\end{aligned}
$$With $m=181.5$, then the linear equation for the number of teenagers having gastric bypass surgery $t$ years since $2000$ takes the form of
$$
y=181.5t+b
.$$Since the line passes through the point $(1,408)$, substitute $t=1$ and $y=408$ in the equation above to solve for $b$. That is,
$$\begin{aligned}
y&=181.5t+b
\\
408&=181.5(1)+b
\\
408&=181.5+b
\\
408-181.5&=b
\\
b&=226.5
.\end{aligned}
$$With $b=226.5$, then the linear equation for the number of teenagers having gastric bypass surgery $t$ years since $2000$ takes the form of
$$
y=181.5t+226.5
.$$
