Thread: Parametric equations 3

If I had a parametric equation of x=-5t-3, y=5t+4, t in R, and I needed to specify the position of a moving point P(x,y) at time t, how would I best describe the behavior of the point as t increases?

1) x decreases, and y decreases.
2) x decreases, and y increases.
3) x increases, and y decreases.
4) x increases, and y increases.

Originally Posted by mike1

If I had a parametric equation of x=-5t-3, y=5t+4, t in R, and I needed to specify the position of a moving point P(x,y) at time t, how would I best describe the behavior of the point as t increases?

1) x decreases, and y decreases.
2) x decreases, and y increases.
3) x increases, and y decreases.
4) x increases, and y increases.

You assume a value of t that is increased over the t in the equations.
(I don't have to do that, but you have to, so that you will understand the solution)
Let us the t in the equations is t=1.
x = -5*1 -3 = -8
Then, we increase t, say t = 3,
x = -5*3 -3 = -18
So, the x decreases as t increases. -------**

Do that on the y.
Old y, when t = 1,
y = 5t +4
y = 5*1 +4 = 9
New y, when t = 3,
y = 5*3 +4 = 19
So, the y increases as the t increases. -----**

Therefore, 2) x decreases, and y increases. -----------answer.