Conversion from Parametric to Vector Form

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Convert the following parametric equations to their equivalent vector form:

\(x = 3 + 2t\), \(y = -1 + 4t\).

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Hint

Recall that the vector form of a line is given by \(\vec{r} = \vec{r_0} + t\vec{d}\), where \(\vec{r_0}\) is the position vector (from the constant terms) and \(\vec{d}\) is the direction vector (from the coefficients of \(t\)).

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Complete Answer

\(\begin{pmatrix} 3 \\ -1 \end{pmatrix} + t \begin{pmatrix} 2 \\ 4 \end{pmatrix}\)

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