Find two sets of parametric equations for the given rectangular equation.
-$$y = 4 x + 6$$
A) $x = t , y = 4 t + 6 ; x = \frac { t } { 4 } , y = t + 6$
B) $x = t , y = 4 t + 6 ; x = 4 t , y = t + 6$
C) $x = t , y = 4 t + 6 ; x = t , y = \frac { t } { 4 } + 6$
D) $x = 4 t , y = t + 6 ; x = \frac { t } { 4 } , y = t + 6$

Question

Quizplus · Accepted Answer

The first set of parametric equations $x = t , y = 4 t + 6$ directly translates the rectangular equation $y = 4x + 6$ by substituting $x$ with $t$. The second set $x = \frac { t } { 4 } , y = t + 6$ also represents the same line because if you solve for $x$ in the first equation, you get $x = \frac{t}{4}$, and substituting this into the original equation gives $y = 4(\frac{t}{4}) + 6 = t + 6$, which matches the second parametric equation.

Find Two Sets of Parametric Equations for the Given Rectangular y=4x+6y = 4 x + 6y=4x+6

Find Two Sets of Parametric Equations for the Given Rectangular $y = 4 x + 6$