To solve for \( y \) in the equation \( 2x + 5y = 10 \), we need to isolate \( y \) on one side of the equation. Here are the steps:

1. **Subtract \( 2x \) from both sides** to move the \( x \)-term to the right:
   \[
   5y = 10 - 2x
   \]

2. **Divide both sides by 5** to solve for \( y \):
   \[
   y = \frac{10 - 2x}{5}
   \]

3. **Simplify the expression**:
   \[
   y = \frac{10}{5} - \frac{2x}{5}
   \]
   \[
   y = 2 - \frac{2}{5}x
   \]

So, the solution for \( y \) is:

\[
\boxed{y = 2 - \frac{2}{5}x}
\]

Would you like more details on the steps, or do you have any questions?

### Relative Questions:
1. How would you solve for \( x \) instead of \( y \) in the equation \( 2x + 5y = 10 \)?
2. What is the slope and y-intercept of the equation \( y = 2 - \frac{2}{5}x \)?
3. How would this equation change if it was given in a different form, such as slope-intercept form?
4. Can you graph the equation \( y = 2 - \frac{2}{5}x \) and identify key points on the graph?
5. How does changing the coefficient of \( x \) in the equation affect the graph?

### Tip:
When solving linear equations, always aim to isolate the variable you're solving for by performing inverse operations step-by-step.

Learn how to solve the equation 2x + 5y = 10 to find the value of y. This problem covers key algebraic concepts, including linear equations and solving for variables. Suitable for students in Grades 7-9.

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