Question

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.

$x=3t+1$,$y=-2t+3$,$t\in \left[0,1\right]$.

Short answer

The required graph is as follows, and its increasing upward.

Step-by-step solution

Step 1. Given Information.

The equations are$x=3t+1$and$y=-2t+3$such that$t\in \left[0,1\right]$.

Step 2. Explanation.

Using equations, make a table that contains the coordinates of several points on the curve.

t	0	1
$x=3t+1$	1	4
$y=-2t+3$	3	1

Step 3. Find the direction.

The direction of motion along the parametric curve with increasing values of t. So it is upward increasing.

The required graph is as follows,