Question

Help with Parametric Equations and Rectangular Equations

Answer 1

Rewrite the parametric equations as a single linear equation.

x = -2t − 1
y = t − 1

Answer 2

x+1=-2t
-1/2x-1/2=t? The question I had is did I transver -2 over correctly?

Answer 3

\(y=t-1\implies t=y+1\) so \(x=-2t-1=-2(y+1)-1\) so \(x+2y=-3\)

Answer 4

I guess if you are confused in one way to do it do it the other way :p

Answer 5

Do you understand what x and y are? and what t represents?

Answer 6

2y=-x-3

Answer 7

t represents the perimeter x = domain y = range

Answer 8

y=-1/2x-3/2?

Answer 9

As t represents the parameter, we are trying to get from a parametric equation, an equation defined by x and y, to a linear equation (or rectangular)

So in solving for out parameter, t, as @oldrin.bataku showed above, you are essentially condensing your two functions of x and y into one linear function

Answer 10

the idea is taht the the parameterization provides us a way to identify every point on the line with a 'coordinate' \(t\) along the line

Answer 11

then by eliminating the parameter we can reduce our system of equations into a single relation between \(x,y\) that is solely satisfied by the points of the line

Answer 12

they are two dsitinct ways of describing the curve; the parameterization gives us a neat way to identify distinct points \((x(t),y(t))\) on the curve by the parameter \(t\) whereas the relationship indirectly or implicitly defines the curve by telling us the fundamental constraint that points \((x,y)\) on the line must satisfy