1. ## Parametric equations 2

I have to select the best description for the curve given by the parametric equation x=t+5, y=2t-1, t in R.

1) a straight line with slope 2.
2) a straight line through the point (5,1).
3) a parabola with vertex (-5,1).
4) a circle centered at (5,-1).

2. Originally Posted by mike1
I have to select the best description for the curve given by the parametric equation x=t+5, y=2t-1, t in R.

1) a straight line with slope 2.
2) a straight line through the point (5,1).
3) a parabola with vertex (-5,1).
4) a circle centered at (5,-1).
When you see a parameter, try to eliminate the parameter. The parameter here is t. So get rid of t.

x = t +5
So, t = x -5 ----------**

y = 2t -1
So,
y = 2(x-5) -1
y = 2x -10 -1
y = 2x -11 --------the equationm where the parameter t was eliminated.

That is a linear equation, a straight line in graph. Its slope is 2, because of the "2x" term.
[y = mx +b, you know.]

Therefore, 1) a straight line with slope 2. --------------answer.

----------------------------
Check "2) a straight line through the point (5,1)."
1 =? 2(5) -11
1 =? 10 -11
1 =? -1
No, so Option (2) is not coorect. Therefore, option (1) is really correct.