Answer
$y=\displaystyle \frac{2}{3}x+\frac{5}{3}$
See image:
Work Step by Step
Build a table of coordinates (x,y)
$x=f(t)=3t+2,\quad \qquad y=g(t)=2t+3$
Plot the points and join with a smooth curve.
Taking the initial t to be the first point in the table, track the direction in which the points "travel" as t increases.
From $ x=3t+2,$
$x-2=3t$
$\displaystyle \frac{x-2}{3}=t,\qquad $which we insert into the parametric equation for y
$y=2t+3\quad $
$y=2\displaystyle \cdot\frac{x-2}{3}+3$
$y=\displaystyle \frac{2}{3}x+\frac{5}{3}$
