To solve the equation \( 10x - 2y = -6 \), let's solve for \( y \) in terms of \( x \).

### Step-by-step:
1. Start with the given equation:
   \[
   10x - 2y = -6
   \]

2. Isolate \( -2y \) by subtracting \( 10x \) from both sides:
   \[
   -2y = -10x - 6
   \]

3. Divide everything by \( -2 \) to solve for \( y \):
   \[
   y = \frac{-10x - 6}{-2}
   \]

4. Simplify the equation:
   \[
   y = 5x + 3
   \]

### Final Solution:
\[
y = 5x + 3
\]

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. What is the slope and y-intercept of the equation \( y = 5x + 3 \)?
2. How would you graph \( y = 5x + 3 \)?
3. Can you rewrite \( 10x - 2y = -6 \) in standard form \( Ax + By = C \)?
4. How does the equation change if the coefficient of \( x \) becomes negative?
5. Solve for \( x \) when \( y = 7 \) in the equation \( y = 5x + 3 \).

**Tip**: When solving for one variable in terms of another, focus on isolating the variable step by step!

Learn how to solve the linear equation 10x - 2y = -6 by converting it into slope-intercept form (y = 5x + 3). This solution includes a step-by-step breakdown of key algebraic concepts, suitable for students in Grades 8-10.

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