(115) Summary of lines

Hi all,

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 y-intercept, or just any generic point (x_1,y_1) 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:

  1. Any two points (x_1,y_1) and (x_2,y_2) on the line gives the slope by \frac{y_2-y_1}{x_2-x_1}
  2. The line is parallel to a line you already know. For example, if your line is parallel to 3x+2y=5, you know your line has slope -\frac{3}{2}, as parallel lines have the same slope.
  3. The line is perpendicular to a line you already know. For example, if your line is perpendicular to 3x+2y=5, you know your line has slope \frac{2}{3}, as perpendicular lines have slopes that multiple to be -1.
Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s