Find Parametric Equations for Functions
-The line segment starting at $( - 6 , - 3 )$ with $t = 0$ and ending at $( - 21 , - 9 )$ with $t = 3$
A) $x = - 5 t - 6 , y = - 2 t - 3$, for $0 \leq t \leq 3$
B) $x = - 2 t - 3 , y = - 5 t - 6$, for $0 \leq t \leq 3$
C) $x = - 6 t - 5 , y = - 3 t - 2$, for $0 \leq t \leq 3$
D) $x = - 3 t - 2 , y = - 6 t - 5$, for $0 \leq t \leq 3$

Question

Quizplus · Accepted Answer

The parametric equations for a line can be found using the formula $x = x_1 + (x_2 - x_1)t$ and $y = y_1 + (y_2 - y_1)t$, where $(x_1, y_1)$ is the starting point and $(x_2, y_2)$ is the ending point. Substituting the given points $(-6, -3)$ for $t=0$ and $(-21, -9)$ for $t=3$, we find the change in $x$ to be $(-21) - (-6) = -15$ and the change in $y$ to be $(-9) - (-3) = -6$. Dividing these by the change in $t$ (3), we get the rates of change: $\frac{-15}{3} = -5$ for $x$ and $\frac{-6}{3} = -2$ for $y$. Thus, the parametric equations are $x = -5t - 6$ and $y = -2t - 3$, valid for $0 \leq t \leq 3$.

Find Parametric Equations for Functions -The Line Segment Starting At (−6,−3)( - 6 , - 3 )(−6,−3)

Find Parametric Equations for Functions
-The Line Segment Starting At $( - 6 , - 3 )$