Find the \( x \)-intercept of the following line. \[ y=-\frac{9}{4} x-1 \] Enter the answer as ordered pair \( (x, y) \).

To find the \( x \)-intercept of the line given by the equation: \[ y = -\frac{9}{4}x - 1 \] the \( x \)-intercept occurs where \( y = 0 \). Set \( y \) to 0 and solve for \( x \): \[ 0 = -\frac{9}{4}x - 1 \] Add 1 to both sides: \[ \frac{9}{4}x = -1 \] Multiply both sides by \( \frac{4}{9} \): \[ x = -\frac{4}{9} \] Therefore, the \( x \)-intercept is at the point \( \left( -\frac{4}{9}, 0 \right) \). **Answer:** \(\left( -\dfrac{4}{9},\ 0 \right)\)