How do you write the corresponding rectangular equation by eliminating the parameter given x=3t-1, y=2t+1?

1 Answer
Dec 2, 2016

# y = 2/3x+4/3 #

Explanation:

#t# is a parameter for #x=x(t)# and #y=y(t#), and in this example it appears once in a linear form, so we can rewrite each equation as:
# x=3t-1 => t=1/3(x+1) #
# y=2t+1 => t=1/2(y-1) #

And then as #t# is the common parameter we can equate these expressions to give:

# 1/2(y-1) = 1/3(x+1) #

Then it is just a case of re-arranging this equation until we get #y=y(x)#

# 3(y-1) = 2(x+1) #
# :. 3y-3 = 2x+1 #
# :. 3y = 2x+4 #
# :. y = 2/3x+4/3 #