The given equation is:

\[
6y - 3x = -12
\]

Let's solve for \( y \) in terms of \( x \).

### Step 1: Isolate the term with \( y \)
To do this, move \( -3x \) to the right side of the equation:

\[
6y = 3x - 12
\]

### Step 2: Solve for \( y \)
Now, divide everything by 6 to solve for \( y \):

\[
y = \frac{3x - 12}{6}
\]

### Step 3: Simplify
We can simplify the fraction:

\[
y = \frac{3x}{6} - \frac{12}{6}
\]

This simplifies to:

\[
y = \frac{x}{2} - 2
\]

So the equation in slope-intercept form is:

\[
y = \frac{x}{2} - 2
\]

This is the final equation for \( y \) in terms of \( x \).

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Do you want further details, or do you have any questions?

Here are some related questions to explore:

1. What is the slope of the line \( y = \frac{x}{2} - 2 \)?
2. How would the graph of this equation look like?
3. What is the \( y \)-intercept of the line?
4. How would you solve for \( x \) if \( y = 4 \)?
5. Can you rewrite the equation in standard form?

**Tip:** To graph a linear equation, start by identifying the slope and the \( y \)-intercept.

Learn how to solve the linear equation 6y−3x=−12 and express it in slope-intercept form y = mx + b. This problem covers key algebraic concepts, including isolating variables and simplifying equations, suitable for students in Grades 7-9.

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