To rewrite the equation \( \frac{1}{4}x - 3y = 4 \) in the slope-intercept form \( y = mx + b \), we need to solve for \( y \). Here are the steps:

1. Start with the given equation:
   \[
   \frac{1}{4}x - 3y = 4
   \]

2. Subtract \( \frac{1}{4}x \) from both sides to isolate the \( y \)-term:
   \[
   -3y = -\frac{1}{4}x + 4
   \]

3. Divide each term by \(-3\) to solve for \( y \):
   \[
   y = \frac{-\frac{1}{4}}{-3}x + \frac{4}{-3}
   \]

4. Simplify the fractions:
   \[
   y = \frac{1}{12}x - \frac{4}{3}
   \]

Therefore, the equation in slope-intercept form is:

\[
y = \frac{1}{12}x - \frac{4}{3}
\]

Here, the slope \( m = \frac{1}{12} \) and the y-intercept \( b = -\frac{4}{3} \).

Would you like more details on any of these steps, or do you have any questions?

### Related Questions:
1. How do you convert a different standard form equation to slope-intercept form?
2. What is the slope-intercept form of a line, and how is it useful?
3. How can you find the x-intercept from the slope-intercept form?
4. What is the difference between slope-intercept form and point-slope form?
5. How do you determine if two lines are parallel or perpendicular using their slopes?

**Tip:** When converting to slope-intercept form, always isolate the \( y \)-term and ensure all terms are simplified.

Learn how to rewrite the linear equation 1/4x - 3y = 4 in slope-intercept form (y = mx + b) with a clear step-by-step guide. This problem covers key algebraic concepts and is suitable for students in Grades 7-9.

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