Convert linear equation -4y=-x+12 into slope intercept form and identify its slope and y- intercept.

To convert the linear equation \(-4y = -x + 12\) into slope-intercept form, we need to solve for \(y\). The slope-intercept form of a line is:

\[
y = mx + b
\]

where:
- \(m\) is the slope
- \(b\) is the y-intercept

### Step-by-Step Solution

1. **Start with the given equation:**

   \[
   -4y = -x + 12
   \]

2. **Divide all terms by \(-4\) to solve for \(y\):**

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

   Simplify the right-hand side:

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

   This simplifies to:

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

3. **Identify the slope and y-intercept:**

   The equation is now in slope-intercept form \(y = mx + b\), where:
   - The slope \(m = \frac{1}{4}\)
   - The y-intercept \(b = -3\)

### Final Answer

- **Slope (m):** \(\frac{1}{4}\)
- **Y-intercept (b):** \(-3\)

Would you like more details on this conversion or any other questions related to linear equations? Here are some related questions you might find interesting:

1. How do you graph a line using the slope and y-intercept?
2. What is the meaning of slope in a linear equation?
3. How can you find the x-intercept of a line from its equation?
4. How do you convert from slope-intercept form to standard form?
5. What are parallel and perpendicular slopes?

**Tip:** When converting equations to slope-intercept form, always isolate \(y\) to make identifying the slope and y-intercept easier.

Convert linear equation -4y=-x+12 into slope intercept form and identify its slope and y-intercept.

Learn how to convert the linear equation -4y=-x+12 into slope-intercept form and identify the slope and y-intercept with a step-by-step solution. This problem covers key algebraic concepts, including the slope-intercept formula and linear equation properties. Suitable for students in Grades 7-9.

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