Find the \( y \)-intercept and \( x \)-intercept of the line. \[ \begin{array}{l}5 x+3 y=-6 \\ y \text {-intercept: } \square \\ x \text {-intercept: } \square\end{array} \]

To find the \( y \)-intercept and \( x \)-intercept of the line given by the equation \( 5x + 3y = -6 \), we can follow these steps: ### Finding the \( y \)-intercept: The \( y \)-intercept occurs when \( x = 0 \). We can substitute \( x = 0 \) into the equation: \[ 5(0) + 3y = -6 \] This simplifies to: \[ 3y = -6 \] Now, divide both sides by 3: \[ y = -2 \] Thus, the \( y \)-intercept is \( -2 \). ### Finding the \( x \)-intercept: The \( x \)-intercept occurs when \( y = 0 \). We can substitute \( y = 0 \) into the equation: \[ 5x + 3(0) = -6 \] This simplifies to: \[ 5x = -6 \] Now, divide both sides by 5: \[ x = -\frac{6}{5} \] Thus, the \( x \)-intercept is \( -\frac{6}{5} \). ### Summary: - \( y \)-intercept: \( -2 \) - \( x \)-intercept: \( -\frac{6}{5} \) Putting it all together, we have: \[ \begin{array}{l} 5x + 3y = -6 \\ y \text{-intercept: } -2 \\ x \text{-intercept: } -\frac{6}{5} \end{array} \]