# Graph the parametric equation x(t)=3t and y(t)=2-2t on [0,1] ?

## Write one Cartesian equation (x and y only) that models this graph. Identify the initial and terminal points. This is for my precalc BC class and I never learned this last year so I appreciate all the help I could get :)

Jul 4, 2018

De-parameterize:

$x = 3 t \implies t = \frac{x}{3}$

$\implies y \left(t\right) = 2 - 2 t q \quad \therefore y \left(x\right) = - \frac{2}{3} x + 2$

For $t \in \left[0 , 1\right]$, then:

• $\left\{\begin{matrix}x \left(0\right) = 3 \cdot 0 = 0 \\ x \left(1\right) = 3 \cdot 1 = 3\end{matrix}\right. q \quad \left\{\begin{matrix}y \left(0\right) = 2 - 2 \cdot 0 = 2 \\ y \left(1\right) = 2 - 2 \cdot 1 = 0\end{matrix}\right.$

graph{y = - 2/3 x + 2 [-1, 4, -1, 3]}

Just be sure to limit yourself to $x \in \left[0 , 3\right]$ when you graph it :)