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 :)

1 Answer
Jul 4, 2018

De-parameterize:

#x = 3t implies t = x/3#

#implies y(t) = 2 - 2t qquad :. y(x) = - 2/3 x + 2 #

For # t in [0,1]#, then:

  • #{(x(0) = 3 * 0 = 0 ),(x(1)= 3*1 = 3):} qquad {(y(0) = 2 - 2 * 0 = 2 ),(y(1)= 2 - 2*1 = 0):}#

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

Just be sure to limit yourself to #x in [0,3]# when you graph it :)