Which set of parametric equations represents the following line or conic?
Use $x = x _ { 1 } + t \left( x _ { 2 } - x _ { 1 } \right)$ and $y = y _ { 1 } + t \left( y _ { 2 } - y _ { 1 } \right)$.
Line: passes through $( 7,6 )$ and $( - 4,3 )$
A)
$\begin{array} { l }
x = - 11 t + 7 \
y = - 3 t + 6
\end{array}$
B)
$x = - 11 t + 7$
$y = 3 t + 6$
C)
$x = - 11 t - 7$
$y = - 3 t - 6$
D)
$x = - 3 t + 6$
$y = - 11 t + 7$
E)
$\begin{array} { l }
x = - 3 t - 6 \
y = - 11 t - 7
\end{array}$

Question

Which set of parametric equations represents the following line or conic?
Use $x = x _ { 1 } + t \left( x _ { 2 } - x _ { 1 } \right)$ and $y = y _ { 1 } + t \left( y _ { 2 } - y _ { 1 } \right)$.
Line: passes through $( 7,6 )$ and $( - 4,3 )$
A)
$\begin{array} { l } 
x = - 11 t + 7 \
y = - 3 t + 6
\end{array}$
B)
$x = - 11 t + 7$
$y = 3 t + 6$
C)
$x = - 11 t - 7$
$y = - 3 t - 6$
D)
$x = - 3 t + 6$
$y = - 11 t + 7$
E)
$\begin{array} { l } 
x = - 3 t - 6 \
y = - 11 t - 7
\end{array}$

Quizplus · Accepted Answer

The correct parametric equations can be found by substituting the given points into the formulas for $x$ and $y$. For $x = x_1 + t(x_2 - x_1)$, using points $(7,6)$ and $(-4,3)$, we get $x = 7 + t(-4 - 7) = 7 - 11t$. For $y = y_1 + t(y_2 - y_1)$, we get $y = 6 + t(3 - 6) = 6 - 3t$. This matches option A.

Which Set of Parametric Equations Represents the Following Line or Conic