Find parametric equations to represent the line segment from $( - 3,4 )$ to $( 12 , - 8 )$. Select the correct answer.
A) $x = - 3 - 15 t , y = 4 - 12 t , 0 \leq t \leq 1$
B) $x = - 3 - 15 t , y = 4 - 12 t , 0 \leq t \leq 2$
C) $x = 8 - 15 t , \quad y = 4 - 12 t , \quad 0 \leq t \leq 2$
D) $x = - 3 + 15 t , y = 4 - 12 t , \quad 0 \leq t \leq 1$
E) $x = 3 + 15 t , \quad y = 4 - 12 t , \quad 0 \leq t \leq 1$

Question

Quizplus · Accepted Answer

The slope of this line segment is $m=\frac{-8-4}{12-(-3)}=-\frac{4}{5}$. Using point-slope form, we have:
$$y-4=-\frac{4}{5}(x+3)$$
Simplifying,
$$y=-\frac{4}{5}x+\frac{8}{5}$$
To make sure we only cover the line segment from $( - 3,4 )$ to $( 12 , - 8 )$, we set up the following inequality:
$$-3\leq x\leq 12\implies-\frac{51}{5}\leq-\frac{4}{5}x+\frac{8}{5}\leq\frac{68}{5}$$
Let $t$ be such that $0\leq t\leq 1$. Then, we have:
$$x=-3+15t,\quad y=4-12t$$
which satisfies the inequality above, and represents the line segment from $( - 3,4 )$ to $( 12 , - 8 )$.

Find Parametric Equations to Represent the Line Segment From (−3,4)( - 3,4 )(−3,4)

Find Parametric Equations to Represent the Line Segment From $( - 3,4 )$