Explanation:

1.  **Recall the definition of a y-intercept:**

    The y-intercept of a graph is the point where the graph crosses the y-axis. This occurs when the x-coordinate is $0$ .

2.  **Substitute $x=0$ into the equation:**

    Given the equation $y = (\dfrac{3}{11})^{x+1}$ .

    Set $x=0$ :

    $y = (\dfrac{3}{11})^{0+1}$

3.  **Simplify the exponent:**

    $y = (\dfrac{3}{11})^{1}$

4.  **Calculate the value of y:**

    $y = \dfrac{3}{11}$

5.  **Write the y-intercept as an ordered pair:**

    Since $x=0$ and $y=\dfrac{3}{11}$, the y-intercept is $(0, \dfrac{3}{11})$.

6.  **Conclusion:**

    The y-intercept of the graph is $(0,\dfrac{3}{11})$ .