y−3= 2 1 ​ x 𝑦

It looks like there are some formatting issues in the equations provided. Here are the corrected equations as I understand them:

1. $y - 3 = \frac{2}{1} x$
2. $y = \frac{1}{2} x + 3$
3. $y = \frac{2}{1} x + 3$

Let's solve each equation step by step.

Equation 1: $y - 3 = \frac{2}{1} x$

This simplifies to:

$y - 3 = 2x$

To solve for $y$:

$y = 2x + 3$

Equation 2: $y = \frac{1}{2} x + 3$

This equation is already solved for $y$.

Equation 3: $y = \frac{2}{1} x + 3$

This simplifies to:

$y = 2x + 3$

Summary of the Equations

1. $y = 2x + 3$
2. $y = \frac{1}{2} x + 3$
3. $y = 2x + 3$

Notice that Equations 1 and 3 are identical, while Equation 2 is different.

If you have any further questions or need more details on these solutions, please let me know. Here are some related questions for further exploration:

1. What is the slope of each line represented by these equations?
2. How do the y-intercepts of these lines compare?
3. What are the intersections of these lines with the x-axis?
4. Can these lines be represented in standard form?
5. How would you graph these lines on the same coordinate plane?
6. What is the significance of the slope in each equation?
7. How do these lines relate to each other on a graph?
8. What happens if you change the constant term in each equation?

Tip: When solving linear equations, always check for simplifications to ensure clarity and correctness in your solutions.