parametric equation 2

Question

Graph the pair of the parametric equation x = 2t y = t + 5, -2 ≤ t ≤ 3

Answer 1

Parametric equation  x = 2t and  y = t + 5 and -2 ≤ t ≤3.

For values of t on the given interval, the parametric equations yield the points (x, y) shown in the table.

t	x = 2t	y = t + 5	(x, y)
-2	x = 2(-2) = -4	y = (-2) + 5 = 3	(-4, 3)
-1	x = 2(-1) = -2	y = (-1) + 5 = 4	(-2, 4)
0	x = 2(0) = 0	y = (0) + 5 = 5	(0, 5)
1	x = 2(1) = 2	y = (1) + 5 = 6	(2, 6)
2	x = 2(2) = 4	y = (2) + 5 = 7	(4, 7)
3	x = 2(3) = 6	y = (3) + 5 = 8	(6, 8)

Graph

1. draw the coordinate plane.

2. Plot the all points.

3. Connected these points with a smooth curve.