Welcome to the first lesson in the Straight Line series!

Over the next few (actually many) lessons, I’ll be covering the various forms of equations to a straight line, and a lot of related concepts, formulas and applications.

Without further ado, let’s get started !

To find the equation to a straight line, we’ll take a general point P(x, y) on the line, and find the relation between the coordinates, which will **always** hold true. (This in fact is the definition of an equation to any curve, as explained here).

We’ll start with the simple ones. Lines which are parallel to the axes.

**1. Equation of a line parallel to the X axis**

A line which is parallel to the X axis will **always **remain at a fixed distance from it. That is, the y-coordinate (i.e. the distance from the X axis) of **any **point P(x, y) will **always **remain the same (and will be equal to that distance)

Therefore the equation of a line parallel to the X axis will be of the form **y = d**, where d is the (signed) distance of the line from the X axis.

**2. Equation of a line parallel to the Y axi****s**

Same here. The x-coordinate of a point on the line (i.e. its distance from the Y axis) will **always** remain the same. Therefore the equation be of the form **x = d**, where d is the (signed) distance of the line from the Y axis.

**3. Equation of the X axis and the Y axis**

Well, what about the equations of the axes themselves? They are lines too, aren’t they? Of course they are !

Following the same method as above, the distance of the X axis from the X axis is… zero !

Therefore its equation is **y = 0 **.Similarly the equation of the Y axis is **x = 0.**

That’s it for now.

Note that, to uniquely describe a line, two conditions were required – the line being parallel to one of the axes, and being at a certain distance from that axis. I’ll come back to this in the subsequent lessons.

**Lesson Summary**

- The equation of a line parallel to the X axis will be of the form
**y = d**, where d is the signed distance of the line from the X axis. - The equation of a line parallel to the Y axis will be of the form
**x = c**, where c is the signed distance of the line from the Y axis. - The equation of the X axis is
**y = 0** - The equation of the Y axis is
**x = 0**

The next lesson will deal with the equations of lines which are not parallel to any of the axes.

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