Graph x=t+1, y=2t-1 for some appropriate range for t.
Interpret. Is there anything to vary to help understand the graph?
The graph of x=t+1, y=2t-1 is shown below with the range [0,1] for t.
Notice that the equations appear to make a line segment. If we try a different range such as [-1,1], let’s see if anything changes?
We still have only a line segment, but now we have some negative values. Let’s increase the range to [-10,10].
A LINE… or is it? After zooming out, we see that we still have a line segment.
Will we always get a segment? Let's try a larger range of t such as 1000.
Well, we get a segment, again. So how can we get a line? We can try setting the two equations x and y equal to each other and solving for t. After doing this, we get:
t=x-1 and t=1/2(y+1)
Now we will graph y=2x+3
We finally get a LINE!! We come to the conclusion that parametric equations are only pieces of a function.
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