Straight Lines – Types, and Real-life Examples

Let us assume that Priyanka travels from Delhi to Noida and covers a distance of ‘x km’, so how do we represent the same?

Well, we know that Math revolves around real-life applications and we can mathematically represent them.

This representation in an image is called a straight line. Now, if I say Priyanka keeps on traveling infinitely to various cities, then we can represent this distance with different straight lines. If the horizontal line is endless, we call it of endless/infinite length.

Similarly, we have other types of straight lines, as shown in the image below:

  Horizontal line _______       Vertical line   |         Slant line  /

From the above text and images, you can see that a straight line doesn’t have a curve, also it doesn’t hold any area or volume, it just carries an infinite length. Now, if I say we can represent straight lines in another way too. So let us discuss that.

Straight Line with Coordinate System

Assume that a lady ‘y’ is three inches taller than twice the height of a man “x”, then we have: y   =   2x + 3

Now, if I say a man a height as x  = 1-inch height, then the height of a woman is 2 * 1 + 3 = 5 inches. Similarly, we get the following values:

So, the coordinates or (x, y) formed from the above value chart are:

1. (0, 3), (assuming a man has no height, then y is 3 inches)
2. (1, 5),
3. (2, 7),
4. (3, 9), and
5. (4, 11).

If we wish to represent these coordinates on a graph, we get straight lines.

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Types of Straight Lines

Types of straight lines in geometry are as follows:

1. Parallel lines
2. Perpendicular lines

Parallel Lines

Let us assume that an equation of a straight line:

Assume that there are two points A and B in line 1 and we represent it by an equation:

If x  = 1, then

y  =

Using the concept of algebra, we form the value chart for the above equation:

Similarly, in line 2: we have the following value chart:

If x  = 1, then

We get

Using the concept of algebra, we form the value chart for the above equation:

Now, we can draw lines 1 and 2 together on a single graph by taking the values from value charts 1 and 2.

Here, we notice that two lines, viz:   and are meeting each other at the very far points that we cannot see, or they meet at infinity.

The category where two straight lines meet at infinity is called parallel lines.

Perpendicular Lines

Assume that line 1 has an equation:

Another line 2 has an equation:

Forming the value chart for line 1:

Forming the value chart for line 2:

Difference Between Parallel Lines and Perpendicular Lines

1. Parallel lines do not meet whereas perpendicular lines meet at an angle of 90 degrees.
2. Parallel lines can be elongated in the same direction whereas perpendicular lines can be extended in the right-angle direction only.

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