Find the slope and \( y \)-intercept of the line. (If an answer does not exist, enter DNE.) \[ x+4 y=0 \] slope \( y \)-intercept \( \quad(x, y)=(\square) \)

To find the **slope** and **\( y \)-intercept** of the line given by the equation: \[ x + 4y = 0 \] we can rewrite the equation in the slope-intercept form, which is: \[ y = mx + b \] where: - \( m \) is the **slope** of the line. - \( b \) is the **\( y \)-intercept** (the point where the line crosses the \( y \)-axis). ### Step 1: Solve for \( y \) Start with the original equation: \[ x + 4y = 0 \] Subtract \( x \) from both sides: \[ 4y = -x \] Divide both sides by 4: \[ y = -\frac{1}{4}x \] Now, the equation is in slope-intercept form: \[ y = -\frac{1}{4}x + 0 \] ### Step 2: Identify the Slope and \( y \)-Intercept - **Slope (\( m \))**: The coefficient of \( x \) is \( -\frac{1}{4} \). \[ \text{Slope} = -\frac{1}{4} \] - **\( y \)-Intercept (\( b \))**: The constant term is \( 0 \), which means the line crosses the \( y \)-axis at \( (0, 0) \). \[ \text{\( y \)-intercept} = (0, 0) \] ### Final Answer - **Slope**: \( -\frac{1}{4} \) - **\( y \)-intercept**: \( (0, 0) \)