Answer
$x+4y-2=0$
See graph
Work Step by Step
We are given the curve in parametric form:
$\begin{cases}
x=4t-2\\
y=1-t
\end{cases}$
with $-\infty\lt t\lt \infty$
Build a table of values:
$t=-2; x=-10; y=3; (x,y)=(-10,3)$
$t=-1; x=-6; y=2; (x,y)=(-6,2)$
$t=0; x=-2; y=1; (x,y)=(-2,1)$
$t=1; x=2; y=0; (x,y)=(2,0)$
$t=2; x=6; y=-1; (x,y)=(6,-1)$
Plot the points and join them to graph the curve:
Determine the rectangular form of the equation:
$t=1-y$
$x=4(1-y)-2$
$x=4-4y-2$
$x+4y-2=0$