This activity is intended to help you explore the standard form of a linear equation.[br][br]In the applet below, we start with a line called L, controlled by a pair of blue points.[br]These two points also control a green "direction vector" for L.[br][list][*]If you add the green ordered pair to one of the blue ordered pairs, you should get the other blue ordered pair.[/*][/list]A second copy of the direction vector starts at the origin.[br][br]To do:[br][list][*]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?[/*][/list]

Here's another applet about the connection between the standard form of a linear equation and the dot product of two vectors.[br][br]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.