Write the corresponding rectangular equation for the curve represented by the parametric equation $x = 9 t - 2 , y = 4 t + 3$ by eliminating the parameter.
A) $4 x - y + 35 = 0$
B) $4 x - 9 y + 35 = 0$
C) $4 x - 9 y + 11 = 0$
D) $4 x + y - 35 = 0$
E) $4 x + 9 y - 11 = 0$

Question

Write the corresponding rectangular equation for the curve represented by the parametric equation $x = 9 t - 2 , y = 4 t + 3$ by eliminating the parameter. 
A) $4 x - y + 35 = 0$
B) $4 x - 9 y + 35 = 0$
C) $4 x - 9 y + 11 = 0$
D) $4 x + y - 35 = 0$
E) $4 x + 9 y - 11 = 0$

Quizplus · Accepted Answer

To eliminate the parameter, we isolate t in one of the equations and substitute it into the other equation:
$$t = \frac{x+2}{9}$$
$$y = 4\left(\frac{x+2}{9}\right) + 3 = \frac{4x+35}{9}$$
Multiplying both sides by 9, we get:
$$4x - 9y + 35 = 0$$
Therefore, the corresponding rectangular equation is  $\boxed{\textbf{(B) }4 x - 9 y + 35 = 0}$.

Write the Corresponding Rectangular Equation for the Curve Represented by the Parametric