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 \( y \)-intercept of the line given by the equation \( 3x - 4y = -16 \), we first need to rewrite the equation in slope-intercept form \( y = mx + b \), where \( m \) represents the slope and \( b \) the \( y \)-intercept. Starting with the equation: \[ 3x - 4y = -16 \] We can solve for \( y \): 1. Subtract \( 3x \) from both sides: \[ -4y = -3x - 16 \] 2. Divide every term by \( -4 \): \[ y = \frac{3}{4}x + 4 \] From this form, we can identify: - The slope \( m \) is \( \frac{3}{4} \). - The \( y \)-intercept \( b \) is \( 4 \). So the answers are: slope: \( \frac{3}{4} \) \( y \)-intercept: \( 4 \)