Adding a border of width $x$ around the entire banner increases each dimension by $2x$, so the new dimensions are $18+2x$ and $10+2x$. Testing the answer choices, when $x=2$, the new dimensions are $22$ and $14$, and

Therefore, the value of $x$ is $2$.

The total cost is the sign-up fee plus the monthly fee times the number of months. So $8+12m=44$, where $m$ is the number of months. Subtract $8$ from both sides to get $12m=36$. Then divide by $12$: $m=3$. Elena paid for $3$ months.

The line crosses the $y$-axis at $4$, so its equation has the form $y=mx+4$. Since the line passes through $(3,10)$, substitute $x=3$ and $y=10$:

Subtract $4$ from both sides:

So $m=2$. The equation is

The line goes through $(0,6)$, so its $y$-intercept is $6$. From $(0,6)$ to $(3,0)$, the change in $y$ is $0-6=-6$ and the change in $x$ is $3-0=3$, so the slope is $\frac{-6}{3}=-2$. Therefore, the equation is $y=-2x+6$, which is equivalent to $y=6-2x$.

The hourly rate is the slope of the line. Using the points $(2,11)$ and $(5,20)$, the change in cost is $20-11=9$ dollars and the change in time is $5-2=3$ hours. So the hourly rate is $\frac{9}{3}=3$ dollars per hour.