Use the first equation and solve it for $y$ in terms of $x$. This will show you the general form of any point on the line.

Once you have $y$ written in terms of $x$, think of $x$ as $r$. What ordered pair $(x,y)$ does that create for an arbitrary real number $r$?

Look at each answer choice and see which one has the same relationship between its two coordinates as the one you found between $x$ and $y$.

Enter 9x + 4y = 18 and -18x - 8y = -36 into Desmos. You should see that the two equations produce exactly the same line (the graphs overlap).

Either do the algebra by hand or in Desmos: rewrite the first equation as y = (-9/4)x + 9/2. This shows the relationship between $x$ and $y$ for every point on the line.

Create a slider r in Desmos. For each answer choice, type its coordinate rule using r in Desmos (for example, (r, expression in r) or (expression in r, r)) and see whether the point always lies on the graphed line as you move the r slider. The correct choice is the one whose point stays on the line for all values of r you test.

Compare the two equations:

If you multiply the first equation by $-2$, you get:

This is exactly the second equation. That means both equations represent the same line, so any solution of one is a solution of the other.

Take the first equation and solve for $y$ in terms of $x$:

Now split the fraction:

So every point on this line has coordinates of the form $(x, -\frac{9}{4}x + \frac{9}{2})$.

We found that any point on the line can be written as $(x, -\frac{9}{4}x + \frac{9}{2})$.

In the answer choices, $r$ is just a placeholder for any real number, the same way $x$ is. So if we let $x=r$, a point on the line becomes

This matches choice $(r,-\frac{9r}{4} + \frac{9}{2})$, which is therefore the correct answer.