### Instruction: For real numbers $t \neq 0,$ the point
\[(x,y) = \left( \frac{t + 1}{t}, \frac{t - 1}{t} \right)\]is plotted.  All the plotted points lie on what kind of curve?

(A) Line
(B) Circle
(C) Parabola
(D) Ellipse
(E) Hyperbola

Enter the letter of the correct option.### Response: So we're given this point: $\left( \frac{t + 1}{t}, \frac{t - 1}{t} \right)$. Let's see what happens when we plug in some values of $t$.
When $t = 1$, the point is $(2,0)$.
When $t = 2$, the point is $(3/2, 1/2)$.
When $t = 3$, the point is $(4/3, 2/3)$.
Notice that the $x$-coordinates are all one more than the $y$-coordinates.
That means the points all lie on the line $y = x - 1$.