Suppose parametric equations for the line segment between $(8,5)$ and $(0,-8)$ have the form: \[ \left\{\begin{array}{l} x(t)=a+b t \\ y(t)=c+d t \end{array}\right. \] If the parametric curve starts at $(8,5)$ when $t=0$ and ends at $(0,-8)$ at $t=1$, then find $a, b, c$, and $d$. \[ \begin{array}{l} a= \\ b= \\ c= \\ d= \end{array} \]

Step 1 ：Suppose parametric equations for the line segment between \((8,5)\) and \((0,-8)\) have the form: \[\left\{\begin{array}{l}x(t)=a+b t \\ y(t)=c+d t\end{array}\right.\]

Step 2 ：If the parametric curve starts at \((8,5)\) when \(t=0\) and ends at \((0,-8)\) at \(t=1\), then we need to find \(a, b, c\), and \(d\).

Step 3 ：The parametric equations for a line segment between two points \((x_1, y_1)\) and \((x_2, y_2)\) can be written as: \[\left\{\begin{array}{l}x(t)=x_1+(x_2-x_1) t \\ y(t)=y_1+(y_2-y_1) t\end{array}\right.\] where \(t\) varies from 0 to 1. At \(t=0\), we are at the point \((x_1, y_1)\) and at \(t=1\), we are at the point \((x_2, y_2)\).

Step 4 ：In this case, \((x_1, y_1) = (8, 5)\) and \((x_2, y_2) = (0, -8)\). So we can substitute these values into the equations to find \(a, b, c\), and \(d\).

Step 5 ：By substituting the values, we get: \[\begin{array}{l}a= \boxed{8} \\ b= \boxed{-8} \\ c= \boxed{5} \\ d= \boxed{-13}\end{array}\]