Look at the first row, where $x=1$ and $y=4$. What is $y/x$ for that pair? Then check if the same value appears for the other given pairs.

Once you know the constant value of $y/x$, rewrite that as an equation in the form $y = (\text{constant}) \cdot x$.

Use your equation to plug in $x=40$ from the last row. The result you get for $y$ is the value of $k$.

In Desmos, type 4/1, 12/3, and 20/5 (you can separate them with commas or enter them one per line). Check that each expression evaluates to the same number; that is your constant ratio $y/x$.

Once you know the constant ratio from Step 1, type that number multiplied by 40 (for example, if the ratio is $r$, type r*40). The result Desmos shows is the value of $k$ in the last row of the table.

The phrase "the ratio of $y$ to $x$ is constant" means that for every pair in the table, the value of $y/x$ is the same number.

So if we compute $y/x$ for each known pair, we should always get the same result.

Use any row with both $x$ and $y$ given. The first row is easiest:

• When $x=1$ and $y=4$, the ratio is

Check another row to confirm the ratio is the same:

• When $x=3$ and $y=12$,

• When $x=5$ and $y=20$,

So the constant ratio $y/x$ is $4$ for every pair, which means $y=4x$ for this relationship.

Since $y/x=4$ for all pairs, we can write:

Multiply both sides by $x$ (for $x \neq 0$) to get:

This equation will give the correct $y$-value for any $x$ in the table.

Now use the equation $y=4x$ for the last row, where $x=40$ and $y=k$.

Substitute $x=40$:

So the missing value is

Therefore, the correct answer is $\boxed{160}$.