Last week we spent some time on lines, and with all the different forms you learned, I think it might be a good time to sum them up a little.
To find a line, you need two pieces of information: the direction of the line, and the position of the line, it doesn’t matter how you get these information. Like making a burger, you need some bread and some patty, it doesn’t matter where you buy the bread and patty.
The position of a line is always given by a point on the line. It might be the -intercept, or just any generic point on the line.
The direction of a line is given by slope (or undefined, in case the line is vertical). It might be directly given to you, and there are many ways of grabbing this information:
- Any two points and on the line gives the slope by
- The line is parallel to a line you already know. For example, if your line is parallel to , you know your line has slope , as parallel lines have the same slope.
- The line is perpendicular to a line you already know. For example, if your line is perpendicular to , you know your line has slope , as perpendicular lines have slopes that multiple to be -1.