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 \( 5x + 6y = 12 \), we can rearrange it into the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. First, isolate \( y \): \[ 6y = -5x + 12 \] \[ y = -\frac{5}{6}x + 2 \] From this, we can see that the slope \( m \) is \( -\frac{5}{6} \) and the \( y \)-intercept \( b \) is \( 2 \). Thus, the \( y \)-intercept in coordinate form is \( (0, 2) \). So, the final answers are: slope: \( -\frac{5}{6} \) \( y \)-intercept \( \quad(x, y)=(0, 2) \)