From the table, when $x$ increases by $2$, $y$ increases by $4$, so the slope is $\frac{4}{2}=2$. That means the equation has the form $y=2x+b$. Using the point $(1,7)$, substitute to get $7=2(1)+b$, so $b=5$. Therefore, the equation is $y=2x+5$.

Add $4$ to both sides of $x-4=9$ to get $x=13$. Therefore, the statement that must be true is $x=13$.

For a rectangle, the perimeter is $2l+2w$. Substitute the given values: $2(9)+2w=30$. This gives $18+2w=30$, so $2w=12$ and $w=6$. The width is $6$ feet.

The line crosses the cost axis at $12$, so the cost is $12$ when $x=0$. It also passes through $(3,27)$, so in $3$ hours, the cost increases from $12$ to $27$. That increase is $27-12=15$ dollars over $3$ hours, so the hourly rate is $\frac{15}{3}=5$ dollars per hour.

The slope of the line is $\frac{10-4}{2-0}=\frac{6}{2}=3$. Since the line passes through $(0,4)$, its $y$-intercept is $4$. So the equation is $y=3x+4$.