In the equation $4x - 7 = 3y$, $y$ is being multiplied by $3$. What operation can you perform on both sides of the equation to get rid of that $3$?

After you divide both sides by $3$, you will get a fraction with $4x - 7$ on top and $3$ on the bottom. Try writing this as two separate terms: one involving $x$ and one constant term. Be careful with the negative sign.

In Desmos, type the original equation exactly as given: 4x - 7 = 3y. Desmos will draw the line that represents this relationship between $x$ and $y$.

On separate lines, type each answer choice (for example, y = (3/4)x - 7/4, y = (4/3)x + 7/3, etc.). You will now see several lines on the same coordinate plane.

Look for the line from the answer choices that lies exactly on top of (coincides with) the graph of 4x - 7 = 3y for all $x$-values. The equation whose graph perfectly overlaps with the original equation’s graph is the correct choice.

"Express $y$ in terms of $x$" means you should rewrite the equation so that $y$ is alone on one side and everything else is written using $x$ on the other side. In other words, you want an equation that looks like $y = (\text{expression with } x)$.

You are given:

$4x - 7 = 3y$.

The $y$ term is $3y$. To isolate $y$, first notice that $3$ is multiplying $y$. To undo this, divide both sides of the equation by $3$:

$\dfrac{4x - 7}{3} = y$.

You can also write this as $y = \dfrac{4x - 7}{3}$.

Now simplify $y = \dfrac{4x - 7}{3}$ by splitting the numerator into two separate fractions:

$y = \dfrac{4x}{3} - \dfrac{7}{3}$.

This makes it clear that the coefficient (slope) in front of $x$ is $\dfrac{4}{3}$ and the constant term (the $y$-intercept) is $-\dfrac{7}{3}$.

From the simplified form, you have:

$y = \dfrac{4}{3}x - \dfrac{7}{3}$.

Compare this with the answer choices and see that it exactly matches choice D, so the correct equation is $y = \dfrac{4}{3}x - \dfrac{7}{3}$.