problem: In the graph below, each grid line counts as one unit. The line shown below passes through the point $(1001,n)$ (not shown on graph).  Find $n$.
  [asy]size(250,0);
  add(shift(-10,-10)*grid(20,20));
  draw((-10,0)--(10,0),linewidth(2));
  draw((0,-10)--(0,10),linewidth(2));
  label("x",(10,0),E);
  label("y",(0,10),N);
  draw((-10,-2.71) -- (10,8.71),blue,Arrows);[/asy]
solution: Looking at the graph, the line has a $y$-intercept of 3.  Also, counting carefully, we can see that when the line travels exactly 7 units horizontally, it travels 4 units vertically.  Therefore, the slope of the line is $4/7$.  So, the equation of the line in slope-intercept form is $y=\frac{4}{7}x+3$.  Substituting 1001 for $x$ and $n$ for $y$, we can find $n$: \begin{align*}
  n&=\frac{4}{7}\cdot 1001 +3\\
  \Rightarrow\qquad n&=4\cdot 143 +3\\
  \Rightarrow\qquad n&=572+3=\boxed{575}.
  \end{align*}