Question

Which of the following equations is on the same path as x=2-3t, y=7-6t?

A. y=3-x
B. y=11+2x
C. y=3+2x
D. y=11-2x
E. y=3-2x

Answer 1

C.
`y = 3+2\cdot x`

Explanation:

Let be the parametric equations
`x = 2-3\cdot t` and
`y = 7 - 6\cdot t`, we need to clear
`t` and eliminate it afterwards to obtain a function of the form
`y = f(x)`:

`x = 2 - 3\cdot t`

`3\cdot t = 2 - x`

`t = (2)/(3)-(1)/(3)\cdot x` (1)

`y = 7 - 6\cdot t`

`6\cdot t = 7 - y`

`t = (7)/(6) - (1)/(6)\cdot y` (2)

By (1) and (2):

`(2)/(3)-(1)/(3)\cdot x = (7)/(6)-(1)/(6)\cdot y`

`4 -2\cdot x = 7 - y`

`y = 3+2\cdot x`

Hence, the correct answer is C.