We are given the equation:

\[
-4x = -2y + 6
\]

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

### Step 1: Isolate the \( -2y \) term

Add \( 2y \) to both sides of the equation:

\[
-4x + 2y = 6
\]

### Step 2: Isolate the \( 2y \) term

To solve for \( y \), we want to isolate the \( y \) term. Subtract \( -4x \) from both sides:

\[
2y = 4x + 6
\]

### Step 3: Solve for \( y \)

Now, divide both sides by 2 to isolate \( y \):

\[
y = \frac{4x + 6}{2}
\]

Simplify the expression:

\[
y = 2x + 3
\]

The equation is now solved for \( y \) in terms of \( x \):

\[
y = 2x + 3
\]

Would you like further details or clarifications on any steps?

Here are 5 related questions to expand on this problem:

1. What is the slope of the line represented by \( y = 2x + 3 \)?
2. How do we graph the equation \( y = 2x + 3 \)?
3. Can you find the x-intercept and y-intercept of this equation?
4. What would the equation look like if the slope were different, say \( y = 5x + 3 \)?
5. How do we find the point of intersection of \( y = 2x + 3 \) with another line?

**Tip:** When solving linear equations, try to get one variable isolated step by step for clarity and simplicity.

This page provides a step-by-step guide to solving the linear equation −4x = −2y + 6 for y in terms of x. Learn how to rearrange and simplify the equation to find y = 2x + 3, with explanations of key algebraic concepts and methods. Ideal for students in Grades 8-10.

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