In $4y - 3x = 12$, what can you add to both sides to remove the $-3x$ from the left side so that only $4y$ remains?

Once you have an equation of the form $4y = \text{(something with } x\text{)}$, what operation do you perform on both sides to solve for just $y$?

In Desmos, type 4y - 3x = 12 as one expression. Desmos will graph the line that represents the original relationship between $x$ and $y$.

On new lines, enter each option exactly as written: y = 3x - 12, y = (12 - 3x)/4, y = 4(3x - 12), and y = (3x + 12)/4. Each one will appear as a separate line on the graph.

Look to see which of the four $y = \dots$ lines lies exactly on top of the graph of 4y - 3x = 12 for all visible points. The option whose graph coincides perfectly with the original line is the equation that correctly expresses $y$ in terms of $x$.

The phrase "expresses $y$ in terms of $x$" means we want an equation that looks like $y = \text{(expression with only } x\text{)}$. So we need to rearrange $4y - 3x = 12$ to get $y$ alone on one side.

Right now, the left side is $4y - 3x$. We want only $y$ (or $4y$) there, so we need to remove the $-3x$ term from the left.

To undo $-3x$, add $3x$ to both sides:

Now the $y$ term is isolated as $4y$.

The equation $4y = 3x + 12$ means $y$ is 4 times smaller than $3x + 12$. To get $y$ alone, divide both sides by 4:

So the equation that expresses $y$ in terms of $x$ is $y = \dfrac{3x+12}{4}$, which corresponds to choice D.