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# (a) Sketch the curve by using the parametric equations to plot points. Indicat with an arrow the direction in which the curve is traced as $t$ increases.(b) Eliminate the parameter to find a Cartesian equation of the curve.$x = 2t - 1$, $\quad y = \dfrac{1}{2}t + 1$

## (a) $$\begin{array}{|c|ccccc|}\hline t & -4 & -2 & 0 & 2 & 4 \\\hline x & -9 & -5 & -1 & 3 & 7 \\\hline y & -1 & 0 & 1 & 2 & 3 \\\hline\end{array}$$(b) $$\begin{array}{l}x=2 t-1 \Rightarrow 2 t=x+1 \Rightarrow t=\frac{1}{2} x+\frac{1}{2}, \text { so } \\y=\frac{1}{2} t+1=\frac{1}{2}\left(\frac{1}{2} x+\frac{1}{2}\right)+1=\frac{1}{4} x+\frac{1}{4}+1 \Rightarrow y=\frac{1}{4} x+\frac{5}{4}\end{array}$$

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

hot, eh? Scratch the curve by using the parametric you wishes to plant points indicated with a narrow the direction in which the curve is traced as tea increases. Hey, wrist like t go too negative to have thanks before too negative. Fast. Why is equal to zero? But he is a courtroom zero. We have actually connected one. Why you can, too. What? But he is equal to axe. Go to three. Why he called too two. He got four, actually, two seven. Why go to three now that sketch the curve. Negative. Five year old year Negative. One one, three, two and seven three says a curve is like this. Andi, it's Cheryl is the direction the bench curve is pressed as tea increases had to be eliminated. Pamper her mentor tto find a petition equation over the cliff. From here we have He is sick or two. Sure why? Wine is too. And then having this equation have axe is a who. Why minus five, this is a condition equation. Now for the crew

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#### Topics

Parametric Equations

Polar Coordinates

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