Explanation:

1.  The slope of a line passing through two points $(x\_1, y\_1)$ and $(x\_2, y\_2)$ is given by the formula $m = \dfrac{y\_2 - y\_1}{x\_2 - x\_1}$.

2.  We are given two points on line k: the x-intercept $(-6,0)$ and the y-intercept $(0,p)$.

    Let $(x\_1, y\_1) = (-6,0)$ and $(x\_2, y\_2) = (0,p)$.

3.  The slope of line k is given as $m = \dfrac{6}{17}$ .

4.  Substitute the points and the slope into the slope formula:

    $\dfrac{6}{17} = \dfrac{p - 0}{0 - (-6)}$

    $\dfrac{6}{17} = \dfrac{p}{0 + 6}$

    $\dfrac{6}{17} = \dfrac{p}{6}$ .

5.  Solve for p by cross-multiplying:

    $6 \times 6 = 17 \times p$

    $36 = 17p$

    $p = \dfrac{36}{17}$ .

Conclusion:

The value of p is $\dfrac{36}{17}$ .