【数学】 直線の方程式 Line equation

A very useful equation which represents a line.

With this form, you can tell that this line goes through point (a, b)

and parallel to

vactor (A, B).

If you are given a line formula of

,

you can automatically tell that this line goes through

point (-2, -1)

and parallel to

vector (3, 4)

Therefore the line is

Usualiy a line is expressed in a form of

.

In this form, the slope is - a/b

Example:

For a line equation of

This line has a slope of 4/3, and y-intercept of 5/3

.

But it is often a bit cumbersome to translate into this equation.

Sometimes it is much easyer to transform the equation,

into

.

Then, you can say,

the line goes through a point (-2, -1) and parallel to vector (3, 4).

Particularly, this form is useful when it comes to 3D line object.

Here goes the main topic of this article.

Guess what kind of line is described by the following equation?

This is a 3D object.

This is a line goes through

point (a, b, c)

and parallel to

vector (A, B, C).

For example

This line goes through a

point (2, 1, 3)

and parallel to

vactor (3, 4, 6)

As such, the line is

Looking from the different angle.

Please note.

A line equation is often coming with "t" like

or

These are the same.

Line.

Don't be panic with the presence of "t".

If you are given formula of

Transform it to

.

Now, you can tell they are just asking a line about

.

In this form , you can imagine the line passing through (2, 1, 3) and parallel to a vector (3, 4, 6).