Question

Eliminating the parameter in the parametric equations x = 5 - 3t, y = 2+t yields what equation?

Answer 1

`y = - x/3 + 11/3`

Explanation:

Because `t` is linear in both expressions we can easily eliminate the parameter as follows:

`x= 5-3t`
`:. 3t = 5-x`
`:. t = (5-x)/3`

`y=2+t`
`t = y-2`

As `t` is the common parameter these two expressions are identical; thus;

`t = (5-x)/3 = y-2`
`y-2 = 5/3 - x/3`
`y = - x/3 + 11/3`

Which is a straight line with gradient `-1/3` and `y`-intercept `11/3`