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A straight line is the second simplest geometric figure and is one-dimensional (it seems to have only length). A straight line is, simply put, an infinitely long straight line that has neither an end nor a beginning.

Basic properties

A straight line is usually written using lower case letters, for example a. A straight line is usually given by two points, since each two points can be drawn by just one straight line. There is also a semi-line, which is similar to a line, except that it has a beginning (but still no end). For example, the arms of angles are made up of half-lines.

Writing a line in the plane

If we are in a plane, we can write a line using a linear function whose graph is always a line. Unfortunately, this method fails in space because you cannot determine the third dimension with a linear function. However, in the plane, writing using a linear function is the easiest way to sleep any line that is not parallel to the axis y. If you have a function specified, you can certainly piece together a line from it easily, but the reverse can be a problem. So let's have a line like this:

The prescription for the linear function looks like this: y = ax + b. First we find b, the absolute term. The easiest way to find it is to read from the graph where the line intersects the y, if x is zero. We can see that it is two, so b = 2. This is because if ax equals zero, the only way to get a two after y in the y = ax + b rule is to make the absolute term equal to two.

Now we have to figure out what a will equal. Now it will be more convenient if we drop the absolute member a for a moment we will assume it is zero. The straight line will then move to the origin of the coordinate system a we will more easily determine a:

We can clearly see that at the point x = 6 y has the value 2. We plug this information into the prescription of the function: 6a + 0 = 2. From this we can easily calculate that $a=\frac26=\frac13$. We have now found the value of a and can write the whole prescription of the function, hence of the line: y=1/3x+2.

$$ y=\frac{x}{3}+2 $$

The relative positions of the lines

Two lines in the plane can have several different relative positions. So let's start with the relative positions in the plane.

If you have two lines that lie on top of each other and merge into one - intersecting at all points, they are called congruent lines. If the lines intersect at a single point, they are called divergent lines. If the lines do not intersect at any point, they are called parallel lines. Parallel lines are usually marked with two such short commas on each line, see the last figure. This is summarised clearly in the following figures:

See the separate article in Analytic Geometry for how to find the relative positions of lines. In the same category, you will also find a procedure to find the general equation of a line, the parametric equation of a line, or the directive form of a line.