# (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.