Straight Line
A straight line or line is an endless onedimensional figure that has no width. The straight line is a combination of endless points joined on both sides of a point. A straight line does not have any curve in it. The straight line can be horizontal, vertical, or slanted. If we draw an angle between any two points on the straight line, we will always get a 180degree. In this minilesson, we will explore the world of straight lines by understanding the equations of straight lines in different formats and how to solve the questions based on straight lines.
Introduction to Straight Line
A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extended to infinity. A straight line is a figure formed when two points \(A (x_1, y_1)\) and \(B (x_2, y_2)\) are connected with the shortest distance between them, and the line ends are extended to infinity.
In the image shown below, a straight line between two points A and B is shown. A straight line AB is represented by: \(\overline{\text{AB}}\)
While straight lines have no definite beginning or end, they are represented in our daytoday lives with examples such as railway tracks or the freeway.
Types of Straight Lines
Straight lines can be of various types. Generally, the straight lines are classified based on their alignment. Their alignment refers to the angle they form with the xaxis or the yaxis. According to the alignment of straight lines, they are of the following types:
 Horizontal lines
 Vertical lines
 Oblique or Slanted lines
Let us explore them one by one.
Horizontal Lines
The lines which are drawn horizontally and are parallel to the xaxis or perpendicular to the yaxis, are called horizontal lines. They form a 0^{o }or 180^{o }angle with the xaxis and a 90^{o} or 270^{o} angle with the yaxis.
In the given figure, \(\overline{\text{AB}}\) is a horizontal line.
Vertical Lines
The lines which are drawn vertically and are parallel to the yaxis, or perpendicular to the xaxis, are called vertical lines. They form a 90^{o }or 270^{o }angle with the xaxis and a 0^{o} or 180^{o} angle with the yaxis.
In the given figure, \(\overline{\text{CD}}\) is a vertical line.
Oblique or Slanted Lines
The lines are drawn in a slanting position or form some angle other than 0^{o}, 90^{o}, 180^{o}, 270^{o}, 360^{o} with the horizontal or vertical lines are called oblique or slanting lines.
In the given figure, \(\overline{\text{EF}}\) and \( \overline{\text{GH}}\) are slanted lines.
Equation of a Straight Line
An equation of a straight line is a linear equation. A straight line on a cartesian plane can have different representations based on the known variables, angles, and constants. The slope of a straight line determines the direction of a straight line and tells how steep the line is. It is calculated as the difference in y coordinates/difference in x coordinates, which is also called rise over run. An equation of a straight line is of various forms. They are as follows:
General Equation of a Straight Line
The general equation of a straight line can be given as ax + by + c = 0, where
 a, b, c are constants, and
 x, y are variables.
 The slope is a/b
Slope and Yintercept Form
A straight line having slope m = tanθ where θ is the angle formed by the line with the positive xaxis, and yintercept as b is given by: y = mx + b, where m is the slope.
Slope Point Form
A straight line having slope m = tanθ where θ is the angle formed by the line with the positive xaxis, and passing through a point \((x_1, y_1)\) is given by: Slope Point Form as \(y  y_1 = m(x  x_1)\)
Two Point Form
A straight line passing through points \((x_1 , y_1)\) and \((x_2 , y_2)\) is given by in the two point form as: \(y  y_1 = (\dfrac{y_2  y_1}{x_2  x_1})(x  x_1)\)
Intercept Form
A straight line having xintercept as a and yintercept as b as shown in the figure below where point A is on the xaxis (vertical here) and point B is on the yaxis (horizontal here), is given in the intercept form by x/a + y/b = 1
Equation of Lines Parallel to Xaxis or Yaxis
The equation of a line parallel to the xaxis is given by: y = ± a, where
 a is the distance of the line from the xaxis. The value of a is + ve if it lies above the xaxis, and n ve if it lies below the xaxis.
The equation of a line parallel to the yaxis. is given by: x = ± b, where
 b is the distance of the line from the yaxis. The value of b is +ve if it lies on the right side of the yaxis, and ve if it lies on the left side of the yaxis.
Below is the image of lines parallel to the xaxis and the yaxis respectively.
Types of Slope
The angle formed by a line with a positive xaxis is the slope of a line. Different lines form different angles with the xaxis. A line can have slopes varying from positive, negative, 0, or even infinite slope. Let's see some of the cases.
Zero Slope
If a line forms a 0^{o} angle with the xaxis, the slope of the line is 0. The slope of a line is represented by, m = tanθ
Here, θ = 0^{o }. Hence m = tan0 = 0. Therefore, a line with the 0 slope is parallel to the xaxis.
Positive Slope
If a line forms an angle that lies between 0^{o} and 90^{o} with the xaxis, the slope of the line is positive.
Negative Slope
If a line forms an angle that lies between 90^{o} and 180^{o} with the xaxis, the slope of the line is negative.
Infinite Slope
If a line forms a 90^{o }angle with the xaxis, or the line is parallel to the yaxis, the slope of the line is not defined or infinite.
As we know, the slope of a line m = tan θ
Here, θ = 90^{o }. slope m = tan 90^{o}, is not defined. Therefore, the line with an infinite slope is parallel to the yaxis.
Properties of a Straight Line
The properties of straight lines are written below.
 A straight line has infinite length. We can never calculate the distance between the two extreme points of the line.
 A straight line has zero areas, zero volume. but it has infinite length.
 A straight line is a onedimensional figure.
 An infinite number of lines can pass through a single point, but there is only one unique line that passes through two points.
Related Topics
Here is a list of related topics to a straight line:
Important Notes
Here is a list of a few points that should be remembered while studying about a straight line:
 A straight line cannot pass through three noncollinear points.
 If two lines l and m coincide, they follow the relation l = k × m, where k is a real number.
 The acute angle \(\theta\) between two lines having slopes \(m_1\) and \(m_2\), where \(m_2 > m_1\) can be calculated using the formula \(tan\theta = \dfrac{m_2  m_1}{1 + m_2 \times m_1}\).
Solved Examples on Straight Lines

Example 1: Paul draws a line on a cartesian plane with the equation y = 2x  1 and his sister draws the line 2y = x + 1, Paul says that the lines intersect in the 2nd quadrant and his sister says that the lines intersect in the 1st quadrant, who is correct.
Solution
Given:
A line drawn by Paul is y = 2x  1his sister drawn the line 2y = x +1
Let's solve these two equations simultaneously to find the point of intersection.
y = 2x  12y = x + 1
When we solve these two equations simultaneously we get
x = 1 and y = 1
Both the line intersect at the point (1, 1)
The point of intersection lies in the first quadrantAnswer: Paul's sister is correct

Example 2: A colony is situated on a cartesian plane, Mathew's house is situated at location (4, 3) and Jim's home is located at (7, 2) two roads have to be constructed from a square located at (3, 2), find out whether these two roads are perpendicular to each other or not (assuming that roads are forming a straight line).
Solution
Let's consider Mathew's house is located at point P (4, 3)
Jim's house is located at point Q (7, 2)
Square is situated at point R (3, 2)
applying the formula to calculate the slope of line between two points
\(m = \dfrac{y_2  y_1}{x_2  x_1}\)
The slope of a line between point P and R is
\(m_1 = \dfrac{3  2}{4  3}\)
\(m_1 = 1\)
The slope of a line between point Q and R is
\(m_2 = \dfrac{2  2}{7  3}\)
\(m_2 = \dfrac{4}{4}\)
\(m_2 = 1\)
If two lines are perpendicular to each other then the product of their slopes is 1.
\(m_1 \times m_2 = 1 \times 1\)
\(m_1 \times m_2 = 1\)Answer: The roads are perpendicular to each other.
Frequently Asked Questions (FAQs)
What Do You Use to Draw a Straight Line?
A straight line can be drawn with the help of a ruler, or t squares, etc. Various geometric tools that have a smooth and flat surface, can also be used to draw a straight line between two points. A straight line that is drawn between two points is known as a line segment. Rulers are the widely used tool to draw a straight line between two points or a straight line in general.
What is the Difference Between Parallel and Perpendicular Lines?
The angle between two parallel lines is 0 degrees, and the angle between two perpendicular lines is 90^{∘}. Parallel lines are aligned in the direction of each other, whereas perpendicular lines are aligned at a 90^{∘} angle with each other. Slopes of the parallel lines are equal to each other whereas the slopes of perpendicular lines are not equal to each other and the slope of one line is equal to the negative inverse of the other line's slope.
What is the Slope of a Straight Line?
The angle formed by a line with a positive xaxis is the slope of a line, different lines from different angles with the xaxis. A line can have slopes varying from positive, negative, 0, or even infinite slope. The slope of a line is specifically measured with the xaxis or a horizontal line. To measure the slope of any line, we draw a horizontal line from any point on the given line and measure the anticlockwise angle from the horizontal line to the given line and then calculate the tanθ of the given angle.
What is the General Equation of a Line?
The general equation of a straight line can be given as ax + by + c= 0, where
 a, b, c are constants, and
 x, y are variables.
What is the Angle Between Two Perpendicular Lines?
The angle between the two perpendicular lines is 90 degrees. The two perpendicular lines are aligned in such a way that the product of the slopes of the two lines is equal to 1. Perpendicular lines are seen everywhere, for example, corner of the table, corner of rooms, etc, and we can measure the angle between the sides and find out that the angle between the perpendicular lines is equal to 90 degrees.
What Are the Parallel Lines?
Two lines are said to be parallel lines if they lie in the same plane and never meet. Parallel lines have a 0degree or 180degree angle difference from each other. They are aligned in the same direction with each other. If we have two parallel lines where the slope of 1 line is known to us, then we can equate the slope of the other line equal to the first line, and find out the slope of the other line.