Lines and directed lines in the plane

### 25.6.1 Lines and directed lines in the plane

See Section 26.4.1 for lines in space.

The line command returns and draws a directed line. It can take its arguments in four different ways.

1. Two points.
   - line takes two arguments: P,Q, two points (which can also be given as a list).
   - line(P,Q) returns and draws the line whose direction is from the P to Q.
2. A point and a slope.
   - line takes two arguments:
     - p, a point.
     - slope=m
   - line(p,slope=m) returns and draws the line through the given point with the given slope, where direction of the line is determined by the slope.
3. A point and a direction vector.
   - line takes two arguments:
     - P, a point.
     - [u1,u2], a direction vector.
   - line(P,[u1,u2]) returns and draws the line through the given point with the direction given by the direction vector.
4. An equation.
   - line takes a x+ b y +c=0, an equation.
   - line(a x+ b y +c=0) returns and draws the line given by the equation. The direction of the line is given by [b,−a].

#### Example

line(0,1+i)

or:

line(1+i,slope=1)

or:

line(1+i,[3,3])

or:

line(y-x=0)

##### Remark.

To draw a line with an additional argument for color (such as color=blue), this argument must be the third argument. In particular, for a list of two points to specify a line in this command, the list must be turned into a sequence, such as with op. For example, given a list L of two points (possibly the result of a different command) which determines a line, to draw the line blue enter line(op(L),color=blue); entering line(L,color=blue) will result in an error.