Answer
$y=\frac{234\,400}{3}t+\frac{5\,729\,000}{3}$
Work Step by Step
Let $t$ be the number of years after the year $2000$ and $y$ be the population of Nevada State. A linear equation that gives the population of Nevada State $t$ years since $2000$ takes the form of
$$
y=mt+b,
$$
where $m$ is the slope and $b$ is the $y$-intercept.
Since in $2010$ (or $10$ years after $2000$), the population is projected at $2691$ thousand, this can be represented by the ordered pair $(t_1,y_1)=(10,2\,691\,000)$. Since in $2025$ (or $25$ years after $2000$), the population is projected at $3863$ thousand, this can be represented by the ordered pair $(t_2,y_2)=(25,3\,863\,000)$.
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,
$$\begin{aligned}
m&=\frac{y_1-y_2}{t_1-t_2}
\\&=
\frac{3\,863\,000-2\,691\,000}{25-10}
\\&=
\frac{1\,172\,000}{15}
\\&=
\frac{234\,400}{3}
.\end{aligned}
$$
With $m=\frac{234\,400}{3}$, then the linear equation that gives the population $t$ years since $2000$ takes the form of
$$
y=\frac{234\,400}{3}t+b
.$$
Since the line passes through the point $(10,2\,691\,000)$, substitute $t=10$ and $y=2\,691\,000$ in the equation above to solve for $b$. That is,
$$\begin{aligned}
y&=\frac{234\,400}{3}t+b
\\
2\,691\,000&=\frac{234\,400}{3}(10)+b
\\
2\,691\,000&=\frac{2\,344\,000}{3}+b
\\
\frac{8\,073\,000}{3}-\frac{2\,344\,000}{3}&=b
\\
b&=\frac{5\,729\,000}{3}
.\end{aligned}
$$
With $b=\frac{5\,729\,000}{3}$, then the linear equation that gives the population $t$ years since $2000$ is
$$
y=\frac{234\,400}{3}t+\frac{5\,729\,000}{3}
.$$
