Answer
$y=\displaystyle \frac{1}{4}x+\frac{5}{4}$
See image:
Work Step by Step
Build a table of coordinates (x,y)
$x=f(t)=2t-1,\displaystyle \quad \qquad y=g(t)=\frac{1}{2}t+1$,
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=2t-1,$
$x+1=2t$
$\displaystyle \frac{x+1}{2}=t,\qquad $which we insert into the parametric equation for y
$\displaystyle \quad y=\frac{1}{2}t+1$
$\displaystyle \quad y=\frac{1}{2}$($\displaystyle \frac{x+1}{2}$)$+1$
$\displaystyle \quad y=\frac{1}{4}x+\frac{5}{4}$
