Find the slope and the \( y \)-intercept of the line. \[ 2 x+8 y=-4 \] Write your answers in simplest form.

To find the slope and the \( y \)-intercept of the line given by the equation \( 2x + 8y = -4 \), we need to rearrange it into the slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. Starting with the equation: \[ 2x + 8y = -4 \] First, isolate \( y \): 1. Subtract \( 2x \) from both sides: \[ 8y = -2x - 4 \] 2. Now, divide every term by \( 8 \): \[ y = -\frac{2}{8}x - \frac{4}{8} \] Simplifying gives us: \[ y = -\frac{1}{4}x - \frac{1}{2} \] Now we can identify the slope and the \( y \)-intercept: - The slope (\( m \)) is \( -\frac{1}{4} \). - The \( y \)-intercept (\( b \)) is \( -\frac{1}{2} \). So, the slope is \( -\frac{1}{4} \) and the \( y \)-intercept is \( -\frac{1}{2} \).