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Let's solve this step by step.

### Step 1: Convert the equation to slope-intercept form (y = mx + b)

We are given the equation:
\[
3x + 4y = 12
\]

To convert it to slope-intercept form (which is \(y = mx + b\)), solve for \(y\):

\[
4y = -3x + 12 \quad \text{(subtract } 3x \text{ from both sides)}
\]
\[
y = \frac{-3}{4}x + 3 \quad \text{(divide everything by 4)}
\]

So, the slope-intercept form of the equation is:
\[
y = \frac{-3}{4}x + 3
\]

### Step 2: Identify the X-intercept and Y-intercept

#### X-intercept:
The X-intercept occurs when \(y = 0\). Substitute \(y = 0\) into the equation:
\[
0 = \frac{-3}{4}x + 3
\]
Solve for \(x\):
\[
\frac{-3}{4}x = -3
\]
\[
x = 4
\]
Thus, the X-intercept is \(x = 4\), or the point \((4, 0)\).

#### Y-intercept:
The Y-intercept occurs when \(x = 0\). Substitute \(x = 0\) into the equation:
\[
y = \frac{-3}{4}(0) + 3 = 3
\]
Thus, the Y-intercept is \(y = 3\), or the point \((0, 3)\).

### Summary:
- **Equation in slope-intercept form:** \(y = \frac{-3}{4}x + 3\)
- **X-intercept:** \(4\)
- **Y-intercept:** \(3\)

Would you like more details on this process or to ask any follow-up questions?

Here are 5 related questions:
1. How do you find the slope from a linear equation?
2. Can we find the slope without converting to slope-intercept form?
3. What does the slope represent in a real-world context?
4. How do the X and Y intercepts help in graphing a line?
5. How can we verify the intercepts using a different method?

**Tip:** The slope tells you how much \(y\) changes for every unit increase in \(x\).

Convert the following equation to slope-intercept form and identify the x and y intercepts. 3x + 4y = 12

Learn how to convert the linear equation 3x + 4y = 12 into slope-intercept form and find the x and y intercepts. Step-by-step solution provided for students in Grades 7-9, covering key concepts in algebra and linear equations.

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