Im back! Um, i have a simple question im trying to get ready for test after 5 days.. I slacked of sadly :( on math, so i have to pick up my skills.. On my test review i have this question:
The parametric equations of a vector are $x_t=3+5t$ and $y_t=-1+3t$. Find the vector equation and the Cartesian equation.
I dont understand above, because i couldnt remember what my teacher told me about this one.. Can somone help me out! Much appreciated for reading thankyou!
Presumably, the vector equation is the vector $r=\left[3+5t,-1+3t\right]$ or the equation $r=\left[5,3\right]t+\left[3,-1\right]$, and the Cartesian equation would just be $y=\frac{3}{5}(x-3)-1$ or $y=\frac{3}{5}x-\frac{14}{5}$. Just solve for the parameter $t$ in the first equation, and then substitute it into the second.
$t=\frac{1}{5}(x_t-3)$, and so $y_t = -1 + 3(\frac{1}{5}(x_t-3))$.