A straight line is a line with no curves, or a structure with infinite length and no curves. A straight line connects both sides. A straight line is a one-dimensional figure that never ends and has no breadth.
Straight Line Equation:
The relationship between the points on a straight line can be determined by solving an equation for the straight line. A straight line’s Slope-Intercept Form is y = mx + c, where m denotes the slope and c denotes the y-intercept. Straight lines are formed by joining points A (x1, y1) and B (x₂, y₂) with the shortest distance between them and both ends stretching to infinity. The traditional form of a linear equation is ax + by = c, where the constants are a, b, and c, and the variables x, y are variables.
Standard Form : axe + by = c .
Slope Form: y = mx + c
Standard Form of Equation of Line:
For a straight line, the typical equation is axe + by = c, where the three variables are real values. As an illustration, let’s look at the usual form of the equation
Example:
y = 2x – 1
We get y – 2x = 2x – 1 – 2x ⇒ y – 2x = -1 after subtracting 2x from both sides of the equation.
We now get the equation of the line in its standard form, which reads 2x – y = 1.
Equation of Straight Line:
All points on the curve are satisfied by the relationship between variables x and y.
The following is the general equation for a straight line:
ax + by + c = 0 (equation of straight line)
Where x, y are variables and a,b, c are constants.
Note 1 – for Horizontal line, slope = 0
Note 2 – If line is ⊥ to x-axis, i.e. vertical then slope is undefined.
Slope= tan Π / 2
Note 3 – If the line is passing through any of two points, then the slope is
tanθ=y₂-y₁ / x₂-x₁
Relations between two lines :
Relation between the two lines is based upon the direction of lines as mentioned below:
Parallel lines: Two lines are parallel if they lie in the same plane and do not
intersect each other. On stretching two parallel lines, a and b; above line is denoted as ‘a’ and the line below is ‘b.’
Two parallel lines is represented as; a‖b.
Perpendicular lines: Two lines are perpendicular if they intersect to form a right angle with each other. On stretching two perpendicular lines, c and d; where the vertical line is ‘c’ and the horizontal line is ‘d’
Two vertical lines is represented as c⟂d.
Conclusion:
A straight line means a collection of all points between and extending beyond two points by definition. An infinite one-dimensional figure, a straight line, has no breadth. Straight lines have no curved sections. Horizontal, vertical, or tilted. A 180-degree angle may be drawn between any two points on a straight line, no matter how far apart they may be. A line is a basic object in most geometries with no formal qualities other than its length, which is its only dimension.