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 $$ 3x - 4y = 12 $$ in **slope-intercept form**, which is $$ y = mx + b $$ (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 $$ y $$:**
   
   Subtract $$ 3x $$ from both sides to move the $$ x $$-term to the right side.
   $$
   -4y = -3x + 12
   $$

3. **Solve for $$ y $$:**
   
   Divide every term by $$ -4 $$ to solve for $$ y $$.
   $$
   y = \frac{-3x}{-4} + \frac{12}{-4}
   $$
   
   Simplify the fractions:
   $$
   y = \frac{3}{4}x - 3
   $$

4. **Final Slope-Intercept Form:**
   $$
   y = \frac{3}{4}x - 3
   $$

**Conclusion:**

The equation $$ 3x - 4y = 12 $$ rewritten in slope-intercept form is:
$$
y = \frac{3}{4}x - 3
$$

Here, the **slope ($$ m $$)** is $$ \frac{3}{4} $$ and the **y-intercept ($$ b $$)** is $$ -3 $$.
To rewrite $$ 3x - 4y = 12 $$ in slope-intercept form, solve for $$ y $$: 1. Subtract $$ 3x $$ from both sides: $$ -4y = -3x + 12 $$ 2. Divide 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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