Find the slope and the \( y \)-intercept of the line. \[ 3 x-4 y=-16 \] Write your answers in simplest form. slope: \( y \)-intercept:

To find the **slope** and the **\( y \)-intercept** of the line given by the equation: \[ 3x - 4y = -16 \] we can rewrite the equation in **slope-intercept form**, which is: \[ y = mx + b \] where: - \( m \) is the **slope** - \( b \) is the **\( y \)-intercept** ### Step-by-Step Solution: 1. **Start with the original equation:** \[ 3x - 4y = -16 \] 2. **Isolate the \( y \)-term:** \[ -4y = -3x - 16 \] 3. **Solve for \( y \) by dividing every term by -4:** \[ y = \frac{-3x - 16}{-4} = \frac{3}{4}x + 4 \] Now, the equation is in slope-intercept form: \[ y = \frac{3}{4}x + 4 \] ### Answers: - **Slope:** \( \frac{3}{4} \) - **\( y \)-intercept:** \( 4 \)