Answer
The parametric equation is, $ x=-2+3t,y=4+3t $
Work Step by Step
Substitute the values of end points $({{x}_{1}},{{y}_{1}})\,\text{ and }\,({{x}_{2}},{{y}_{2}})$ into the standard equation:
$x={{x}_{1}}+t( {{x}_{2}}-{{x}_{1}}),$
$y={{y}_{1}}+t( {{y}_{2}}-{{y}_{1}})$
Plug in:
$\begin{align}
& x=-2+t\left( 1+2 \right),y=4+t\left( 7-4 \right) \\
& x=-2+t\left( 3 \right),y=4+t\left( 3 \right) \\
& x=-2+3t,y=4+3t \\
\end{align}$
Thus, $ x=-2+3t,y=4+3t $ is a set of parametric equations.
