Linear Equations: The Standard Form
This activity is intended to help you explore the standard form of a linear equation.
In the applet below, we start with a line called L, controlled by a pair of blue points.
These two points also control a green "direction vector" for L.
- If you add the green ordered pair to one of the blue ordered pairs, you should get the other blue ordered pair.
- Play with the blue points.
- Check the arithmetic on the vector, if you like.
- Gradually move the slider at the top of the applet.
- What do you notice?
Here's another applet about the connection between the standard form of a linear equation and the dot product of two vectors.
The main question is: for which vectors B is the dot product A.B close to 0? The gold region is supposed to help you spot it.