need help with parameter

Question

Eliminate the parameter t to find a Cartesian equation in the form for:

x(t)=-3t

y(t)=-8+2t

The resulting equation can be written as = 

Answer 1

x(t) = -3t; y(t) = -8 + 2t

Method 1:

Make the parameter t the subject of the x component equation,

x = -3t

t = -x/3

Then, substitute in the y(t) equation and solve for x:

y = -8 + 2(-x/3)

y = -8 - 2x/3

y + 8 = -2x/3

-2x = 3(y + 8)

x = (-3/2)(y + 8)

x(y) = -(3/2)y - 12

Method 2:

Make the parameter t the subject of the y component equation,

y = -8 + 2t

y + 8 = 2t

t = (y + 8)/2

Then, substitute in the x(t) equation:

x = -3[(y + 8)/2]

x(y) = -(3/2)y - 12