Question

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

Answer 1

Answer:

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

Step-by-step 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 $y = f(x)$:

$x = 2 - 3\cdot t$

$3\cdot t = 2 - x$

$t = \frac{2}{3}-\frac{1}{3}\cdot x$ (1)

$y = 7 - 6\cdot t$

$6\cdot t = 7 - y$

$t = \frac{7}{6} - \frac{1}{6}\cdot y$ (2)

By (1) and (2):

$\frac{2}{3}-\frac{1}{3}\cdot x = \frac{7}{6}-\frac{1}{6}\cdot y$

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

$y = 3+2\cdot x$

Hence, the correct answer is C.