Question

Explain how you would graph the following set of parametric equations by plotting points and describing the orientation. x = 3t and (4 points)

Answer 1

To graph the parametric equations x = 3t, we need to plot points by choosing values for t and then calculating the corresponding x coordinate.

Let's choose values of t as 0, 1, -1, and 2:

When t = 0, x = 3(0) = 0. So the point (0,0) is on the graph.
When t = 1, x = 3(1) = 3. So the point (1,3) is on the graph.
When t = -1, x = 3(-1) = -3. So the point (-1, -3) is on the graph.
When t = 2, x = 3(2) = 6. So the point (2, 6) is on the graph.

Once we have plotted these points, we can see that they form a straight line that passes through the points (0,0), (1,3), (-1,-3), and (2,6). The orientation of the line is diagonal from the bottom left to the top right corner of the graph.