To write the equation $2y = 3x + 4$ in standard form, we need to rearrange it into the format:

$Ax + By = C$

Where $A$, $B$, and $C$ are integers, and $A$ is positive.

Let's rewrite the equation:

$2y = 3x + 4$

First, subtract $3x$ from both sides to move the $x$-term to the left:

$-3x + 2y = 4$

To make the coefficient of $x$ positive, multiply the entire equation by $-1$:

$3x - 2y = -4$

Thus, the equation in standard form is:

$3x - 2y = -4$

Would you like further details or have any questions?

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Here are 5 related questions to deepen your understanding:

1. How do you convert an equation from slope-intercept form to standard form?
2. What is the significance of the coefficients in standard form equations?
3. How would you graph an equation given in standard form?
4. How can you verify that an equation is correctly written in standard form?
5. What happens if you divide or multiply both sides of the equation by a constant?

Tip: When converting to standard form, make sure the coefficient of $x$ is positive, and the coefficients are simplified as much as possible.