Let's solve the equation \(-10x + 2y = 12\) step by step. Since it's a linear equation in two variables (\(x\) and \(y\)), we can express one variable in terms of the other.

### Solving for \(y\) in terms of \(x\):
1. Start with the given equation:
   \[
   -10x + 2y = 12
   \]
2. Isolate \(2y\) by adding \(10x\) to both sides:
   \[
   2y = 10x + 12
   \]
3. Now, divide both sides by 2 to solve for \(y\):
   \[
   y = 5x + 6
   \]

So, the solution in terms of \(y\) is:
\[
y = 5x + 6
\]

This represents a straight line equation where \(y\) depends on the value of \(x\). You can now substitute any \(x\) value to find corresponding \(y\) values.

Would you like further details on solving this, or do you have any questions?

### Related questions:
1. How would you solve for \(x\) in terms of \(y\) from this equation?
2. What is the slope of the line described by this equation?
3. How would you graph the line of this equation?
4. Can we check any specific \(x\) and \(y\) pair that satisfies the equation?
5. How does changing the constant \(12\) in the original equation affect the solution?

**Tip:** Linear equations in two variables represent straight lines in a coordinate plane, with a constant slope.

Learn how to solve the linear equation -10x + 2y = 12 by isolating variables and expressing the equation in slope-intercept form (y = mx + b). Suitable for students in Grades 7-9, this problem introduces key algebraic concepts and provides a detailed step-by-step solution.

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