Answer:
C. [tex]y = 3+2\cdot x[/tex]
Step-by-step explanation:
Let be the parametric equations [tex]x = 2-3\cdot t[/tex] and [tex]y = 7 - 6\cdot t[/tex], we need to clear [tex]t[/tex] and eliminate it afterwards to obtain a function of the form [tex]y = f(x)[/tex]:
[tex]x = 2 - 3\cdot t[/tex]
[tex]3\cdot t = 2 - x[/tex]
[tex]t = \frac{2}{3}-\frac{1}{3}\cdot x[/tex] (1)
[tex]y = 7 - 6\cdot t[/tex]
[tex]6\cdot t = 7 - y[/tex]
[tex]t = \frac{7}{6} - \frac{1}{6}\cdot y[/tex] (2)
By (1) and (2):
[tex]\frac{2}{3}-\frac{1}{3}\cdot x = \frac{7}{6}-\frac{1}{6}\cdot y[/tex]
[tex]4 -2\cdot x = 7 - y[/tex]
[tex]y = 3+2\cdot x[/tex]
Hence, the correct answer is C.
