**Collaborative effort by Adeya Powell and Laura Trkovsky**

** **

**Parametric Curves**

Graph

for some appropriate
range for **t**.

Interpret. Is there
anything to vary to help understand the graph?

** **

LetÍs start making some conjectures:

I believe the graph will be line because
t+1 and 2t+1 are both graphs of a line.

LetÍs see if we can line the x and y
intercepts:

Y=mx+b is the slope intercept form of a
line.

therefore, 2t-1=m*(t+1) +b

__Finding the y-intercept:__

x=0 when t=-1

when x=0, b=2t-1 but t=-1, therefore b=-3.

(0,-3) is the y intercept.

__Where does the line? hit the
x-intercept:__

Y=0 when t=1/2

X=1/2 +1=1.5

(1.5,0)

LetÍs now look at the graph,

We were correct about the intercepts. The
t values went from

-44. So the y values would go from -97.

If we increase the values for t, we would
lengthen the line. If we decrease the value for t, we would shorten the line.

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