https://file.aiquickdraw.com/mathbot/file/17300484659631c6i41vh.jpg

Which equations are equivalent to the equation above?

The equation in the image is:

\[
6x - 2y = 12
\]

To find equivalent equations, we can simplify or manipulate this equation without changing its solution set. One common approach is to divide all terms by a common factor. In this case, we can divide by \(2\) to simplify.

1. **Divide by 2**:
   \[
   \frac{6x}{2} - \frac{2y}{2} = \frac{12}{2}
   \]
   which simplifies to:
   \[
   3x - y = 6
   \]

So, \(3x - y = 6\) is an equivalent form of \(6x - 2y = 12\).

Other equivalent forms can be generated by further operations, such as rearranging terms or multiplying both sides by a constant.

Would you like more examples of equivalent forms, or have any specific questions?

### Related Questions
1. What would happen if we multiplied both sides of \(3x - y = 6\) by a different number?
2. How can we express this equation in slope-intercept form?
3. What is the slope of the line represented by this equation?
4. How do we graph the line for this equation?
5. Can we find the x- and y-intercepts of this equation?

### Tip
When looking for equivalent equations, any operation that affects both sides equally (like multiplying, dividing, or rearranging) will maintain the equation's equivalence.

Explore how to find equations equivalent to 6x - 2y = 12 using simplification techniques. Learn about key algebraic concepts, such as linear equations and properties of equality. This guide is suitable for students in Grades 8-10.

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