Find the slope and \( y \)-intercept of the line. (If an answer does not exist, enter DNE.) \[ 5 x+6 y=12 \] slope \( y \)-intercept \( \quad(x, y)=(\square \)

To find the **slope** and **\( y \)-intercept** of the line given by the equation: \[ 5x + 6y = 12 \] **1. Solve for \( y \) in terms of \( x \) to get the equation in slope-intercept form (\( y = mx + b \)):** \[ \begin{align*} 5x + 6y &= 12 \\ 6y &= -5x + 12 \\ y &= -\frac{5}{6}x + 2 \end{align*} \] **2. Identify the slope (\( m \)) and \( y \)-intercept (\( b \)):** - **Slope (\( m \))**: The coefficient of \( x \) is \( -\frac{5}{6} \). \[ \text{Slope} = -\frac{5}{6} \] - **\( y \)-intercept (\( b \))**: The constant term is \( 2 \), which corresponds to the point \( (0, 2) \) on the graph. \[ \text{\( y \)-intercept} = (0, 2) \] **Final Answer:** - **Slope:** \( -\dfrac{5}{6} \) - **\( y \)-intercept:** \( (0,\ 2) \)