$x$ and $y$ parameterised in terms of the variable $t$.

Question

If I have a function $$y=\frac 1 3 x+ \frac{11}{3}$$

The bounds are from $(-2,3)$ to $(1,4)$

1) How do I put $x$ and $y$ in terms of a third variable $t$

2) what will be the bounds of such a equation?

So Far I have, that if we let $-2 \le t \le 1$, we can write: $$ x(t)=t \text{ and } y(t)=\frac13t+\frac{11}{3} $$

Answer 1

Yes that correct, as an alternative we can also take for example

• $x(t)=3t$
• $y(t)=t+\frac{11}3$

for $x\in(-2/3,1/3)$.