Question

How do you write the corresponding rectangular equation by eliminating the parameter given x=3t-1, y=2t+1?

Answer 1

`y = 2/3x+4/3`

Explanation:

`t` is a parameter for `x=x(t)` and `y=y(t`), and in this example it appears once in a linear form, so we can rewrite each equation as:
`x=3t-1 => t=1/3(x+1)`
`y=2t+1 => t=1/2(y-1)`

And then as `t` is the common parameter we can equate these expressions to give:

`1/2(y-1) = 1/3(x+1)`

Then it is just a case of re-arranging this equation until we get `y=y(x)`

`3(y-1) = 2(x+1)`
`:. 3y-3 = 2x+1`
`:. 3y = 2x+4`
`:. y = 2/3x+4/3`