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# Write parametric, equations for the given curve for the given definitions y = -4x + 1 a) x = t b) x= frac{t}{2} c) x = -4t # Write parametric, equations for the given curve for the given definitions y = -4x + 1 a) x = t b) x= frac{t}{2} c) x = -4t

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Parametric equations, polar coordinates, and vector-valued functions asked 2020-11-06
Write parametric, equations for the given curve for the given definitions $$y =\ -4x\ +\ 1$$ a) $$x = t$$ b) $$x=\ \frac{t}{2}$$ c) $$x =\ -4t$$

## Answers (1) 2020-11-07
a.)$$x = t$$
$$y =\ −4x\ +\ 1$$ substituting$$x\ −\ y =\ −4(t)\ +\ 1$$
$$y =\ −4t\ +\ 1$$ Hence parametric equations are: $$y =\ −4t\ +\ 1\ and\ x = t$$ b.)$$x =\ \frac{t}{2}$$
$$y =\ −4x\ +\ 1$$ substituting x: $$y =\ −4(\frac{t}{2})\ +\ 1y =\ −2t\ +\ 1$$ hence the parametric equations are: $$y =\ −2t\ +\ 1x =\ \frac{t}{2}$$ Step 2 c.)$$x =\ −4t$$
$$y =\ −4x\ +\ 1$$ substituting x: $$y =\ −4(−4t)\ +\ 1y = 16t\ +\ 1$$ Hence parametric equation are: $$y = 16t\ +\ 1x =\ −4t$$

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