The scale is $1$ inch for every $4$ feet. Since the flower bed measures $3.5$ inches on the drawing, multiply $3.5$ by $4$ to find the actual length: $3.5\times 4=14$. Therefore, the actual length of the flower bed is $14$ feet.

The ratio is 2 cups for every 5 cats. Since 20 cats is $4$ times as many as 5 cats, multiply the amount of food by $4$: $2\times 4=8$. So 20 cats need $8$ cups of dry food.

The line passes through $(0,2)$ and $(4,10)$, so its constant rate of change is

This means $y$ increases by 2 for each increase of 1 in $x$. Starting from $x=4$ and $y=10$, moving to $x=7$ is an increase of 3 in $x$, so $y$ increases by $2\cdot 3=6$. Therefore,

The map scale gives a ratio of $2$ inches for every $15$ miles. To find the map distance for $35$ miles, multiply $35$ by the conversion factor $\frac{2\text{ inches}}{15\text{ miles}}$. This gives $35\cdot \frac{2}{15}=\frac{70}{15}$ inches. So the correct expression is $\frac{2}{15}\cdot 35$.

The cost per notebook is the unit rate, which is the change in total cost divided by the change in number of notebooks. Using the points $(2,6)$ and $(5,15)$, the change in cost is $15-6=9$ dollars and the change in notebooks is $5-2=3$. So the cost per notebook is $\frac{9}{3}=3$ dollars. Therefore, the correct answer is $3$.