What will the graph of this parametric equation look like?

Question

What will the graph of this parametric equation look like?

$$x = 2t$$ $$y = t + 5, \quad -2 ≤ t ≤ 3$$

Does "$-2 ≤ t ≤ 3$" represent the domain?

Answer 1

Yes, it means that you will only consider values of $t$ ranging from $-2$ to $3$, although the expressions make sense for all $t$. Notice that $-2 \leq t \leq 3 \implies -4\leq 2t \leq 6$, that is, $-4 \leq x \leq 6$. Eliminating $t$ from these expressions, we obtain $$y = \frac{x}{2}+5,$$ a line segment in the plane, joining the points $(-4,3)$ and $(6,8)$.