Step 1:
The line segment starting at \(P(-1,\ -3)\ \text{and ending at}\ Q(6,\ -16)\). We have to find the parametric equations for this line segment.
Step 2:
The parametric equations for a line segment starting from P and ending at \(Q\ is\ P\ +\ tQ\).
Step 3:
The parametric equations of the line segment starting at \(P(-1,\ -3)\ \text{and ending at}\ Q(6,\ -16)\ is\)

\(P\ +\ tQ = (−1,\ −3)\ +\ t (6,\ −16) = (−1\ +\ 6t,\ −3\ −\ 16t)\)

\(\therefore\ x=\ -1\ +\ 6t,\ y=\ -3\ -\ 16t\)

\(P\ +\ tQ = (−1,\ −3)\ +\ t (6,\ −16) = (−1\ +\ 6t,\ −3\ −\ 16t)\)

\(\therefore\ x=\ -1\ +\ 6t,\ y=\ -3\ -\ 16t\)