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

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 \( -3 \).