To convert the equation \(-4x + 4y = 12\) into slope-intercept form, we need to solve for \(y\) in terms of \(x\).

### Steps:
1. Start with the given equation:
   \[
   -4x + 4y = 12
   \]

2. Add \(4x\) to both sides to isolate terms with \(y\):
   \[
   4y = 4x + 12
   \]

3. Divide each term by \(4\) to solve for \(y\):
   \[
   y = x + 3
   \]

### Result:
The slope-intercept form is:
\[
y = x + 3
\]
where the slope \(m = 1\) and the y-intercept \(b = 3\).

Would you like further details or have any questions?

### Further Questions:
1. How can I graph this line using the slope and y-intercept?
2. What would happen to the slope if the equation was \(-4x + 8y = 12\)?
3. How can I determine if two lines are parallel given their equations?
4. How do you convert from slope-intercept form back to standard form?
5. What are the effects of changing the y-intercept in a linear equation?

### Tip:
In the slope-intercept form, the coefficient of \(x\) represents the slope, showing how steep the line is.

Explore the steps to convert the equation -4x + 4y = 12 into slope-intercept form, identifying the slope and y-intercept. This problem covers essential algebraic concepts such as linear equations and slope-intercept form, suitable for Grades 7-9.

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