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WZ
Numerade Educator

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Problem 5 Medium Difficulty

(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 $

Answer

(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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Video Transcript

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