Find the \( x \)-intercept and the \( y \)-intercept without graphing. \[ 2 y-8=3 x \] \( x \)-intercept \( \quad(x, y)=(\square) \) \( y \)-intercept \( \quad(x, y)=(\square) \)

To find the \( x \)-intercept, set \( y = 0 \) in the equation \( 2y - 8 = 3x \): \[ 2(0) - 8 = 3x \implies -8 = 3x \implies x = -\frac{8}{3}. \] Thus, the \( x \)-intercept is \( (x, y) = \left(-\frac{8}{3}, 0\right) \). To find the \( y \)-intercept, set \( x = 0 \): \[ 2y - 8 = 3(0) \implies 2y - 8 = 0 \implies 2y = 8 \implies y = 4. \] Thus, the \( y \)-intercept is \( (x, y) = (0, 4) \). \( x \)-intercept \( \quad(x, y) = \left(-\frac{8}{3}, 0\right) \) \( y \)-intercept \( \quad(x, y) = (0, 4) \)