The task is to convert the given equations into slope-intercept form, which is of the form $y = mx + b$, where $m$ is the slope, and $b$ is the y-intercept.

Let's work through both equations:

A) $2x + 2y = 10$

1. To convert this into slope-intercept form, isolate $y$ on one side. $2y = -2x + 10$
2. Now, divide both sides by 2 to solve for $y$: $y = -x + 5$ So, the slope-intercept form for A is $y = -x + 5$.

B) $12 + 4y = -4x$

1. First, subtract 12 from both sides: $4y = -4x - 12$
2. Now, divide the entire equation by 4 to isolate $y$: $y = -x - 3$ So, the slope-intercept form for B is $y = -x - 3$.

Would you like any additional details or explanations?

Here are 5 related questions to expand your understanding:

1. What is the slope and y-intercept for equation A?
2. How would you graph the line for equation B?
3. Can you find the x-intercept for both equations?
4. What happens if you change the slope in these equations?
5. How do parallel lines relate to their slopes?

Tip: To quickly identify the slope, look at the coefficient of $x$ after converting to slope-intercept form.