`x=5-4t, y=2+5t` Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.

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`x = 5-4t`


To graph a parametric equation, assign values to t. Since there is no given interval for t, let's consider the values from t=-3 to t=3.


`x=5-4(-3) = 17`

`y= 2+5(-3) = -13`



















And, plot the points (x,y) in the xy-plane.   

(Please see attachment for the orientation of the curve.)

Take note that the graph of a parametric equation has direction. For this equation, as the value of t increases, the points (x,y) are going to upward to the left.

To convert a parametric equation to rectangular form, isolate the t in one of the equation. Let's consider the equation for x.

`x= 5-4t`



Then, plug-in this to the other equation.





`y=2-(5x - 25)/4`


`y=(33 - 5x)/4`

`y=-(5x)/4 + 33/4`

Therefore, the rectangular form of the given parametric equation is `y=-(5x)/4 + 33/4` .

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