Rewrite the equation $$ 3 x-4 y=12 $$ in slope-intercept form, solving for $$ y $$. Show your work.

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To rewrite the equation $$ 3x - 4y = 12 $$ into **slope-intercept form** ($$ y = mx + b $$), where $$ m $$ is the slope and $$ b $$ is the y-intercept, follow these steps:

1. **Start with the original equation:**
   $$
   3x - 4y = 12
   $$

2. **Isolate the term containing $$ y $$ by moving $$ 3x $$ to the other side:**
   $$
   -4y = -3x + 12
   $$

3. **Solve for $$ y $$ by dividing every term by $$ -4 $$:**
   $$
   y = \frac{-3x + 12}{-4}
   $$

4. **Simplify the equation:**
   $$
   y = \frac{3}{4}x - 3
   $$

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

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

This means the line has a slope of $$ \frac{3}{4} $$ and crosses the y-axis at the point $$ (0, -3) $$.
To rewrite $$ 3x - 4y = 12 $$ in slope-intercept form, solve for $$ y $$: 1. Subtract $$ 3x $$ from both sides: $$ -4y = -3x + 12 $$ 2. Divide every term by $$ -4 $$: $$ y = \frac{3}{4}x - 3 $$ So, the slope-intercept form is: $$ y = \frac{3}{4}x - 3 $$

Rewrite the equation in slope-intercept form, solving for . Show your work.

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