### Home > PC > Chapter 10 > Lesson 10.1.4 > Problem10-58

10-58.

Find the vector equation of the line through the points $\left(2, 3\right)$ and $\left(4, −1\right)$. Write your answer using unit vectors $\textbf{i}$ and $\textbf{j}$.

Review your work from problem 10-52.

Find the vector between the two given points.

$\left. \begin{array} { c } { \langle 4 - 2 , - 1 - 3 \rangle } \\ { \langle 2 , - 4 \rangle } \end{array} \right.$

The vector equation of the line uses a point on the line and the vector between the given points.

$\langle 2,3 \rangle + t \langle 2 , - 4 \rangle$

We need a vector with $\textbf{i}$, $\textbf{j}$ components. Simplify the expression and rewrite it with $\textbf{i}$ and $\textbf{j}$.

$\left(2 + 2t\right)\textbf{i} + \left(3 − 4t\right)\textbf{j}$