Question

Make a table of values and graph the parametric equations using t values from 0 to 5:

Xt = t - 3
Yt = 2t - 2

Answer 1

The table of values for the parametric equations Xt = t - 3 and Yt = 2t - 2 from t = 0 to 5 includes the points (-3,-2), (-2,0), (-1,2), (0,4), (1,6), and (2,8). These points are plotted on a graph to show the dependence of y on x.

Step-by-step explanation:

Creating a Table of Values for Parametric Equations

To graph the parametric equations Xt = t - 3 and Yt = 2t - 2 using t values from 0 to 5, we will create a table of values. Substitute each t value into the equations to find the corresponding x and y coordinates.

tXtYt0-3-21-202-12304416528

Now, using these points, we can plot them on a graph and connect them to visualize the dependence of y on x. Each (Xt,Yt) pair corresponds to a point on the graph which, when connected, illustrates the trajectory of the parametric equations over the specified range of t values.