# The Vector Equation of a Line

- Author:
- Michelle Krummel, John Fitzgerald

This investigation looks at the vector equation of a line. The construction is defined by some key points.
The line passing through points A and R is parallel to vector

**b**. The points A and R are fixed to the line.Thinking critically about your previous knowledge of vectors, explore the following applet by moving around points R, A, and the end points of

**b**whilst observing the the information given in the algebra view. Answer the following questions. 1. What is the algebraic relationship between vector**b**and vector**AR**? 2. Can you define the vector**r**in terms of the vector**a**and the vector**AR**? 3. What does**a**represent in general terms? 4. What comparisons can you make between your answer to question 2 and the equation for a line (y=mx + c)?