The equation \( 5x + 10 = 10y \) is a linear equation in two variables, \(x\) and \(y\). Let's solve for \(y\) in terms of \(x\).

### Steps:
1. **Subtract 10 from both sides** to isolate the term with \(y\) on the right side:
   \[
   5x = 10y - 10
   \]
   
2. **Rearrange the equation** by adding 10 to both sides:
   \[
   5x = 10y
   \]
   
3. **Divide both sides by 10** to solve for \(y\):
   \[
   y = \frac{5x}{10} = \frac{x}{2}
   \]

Thus, the equation in terms of \(y\) is:
\[
y = \frac{x}{2}
\]

This equation represents a line with slope \(\frac{1}{2}\) and a y-intercept of 0.

Do you have any questions or need further details?

Here are 5 related questions you could explore:
1. What is the slope and intercept form of a line?
2. How do you find the slope between two points on a line?
3. How would you graph the equation \(y = \frac{x}{2}\)?
4. Can we rewrite the equation in terms of \(x\)?
5. What is the relationship between \(x\) and \(y\) for different values of \(x\)?

**Tip**: When solving for one variable in terms of another, always aim to isolate the variable by reversing operations step by step.

Learn how to solve the linear equation 5x + 10 = 10y. This detailed step-by-step solution explores key algebraic concepts like linear equations, slope-intercept form, and solving for y in terms of x. Suitable for students in Grades 8-10.

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