## Precalculus (6th Edition) Blitzer

The parametric equation is, $x=-2+3t,y=4+3t$
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.