The equation of Line

The line is the Basic element of geometry where we learn about many types of lines such as parallel lines, perpendicular lines, intersecting lines etc, these lines are important to draw various kinds of polygon shapes. For example; To draw A square, we need four lines of equal length joined by end to end.

Now, Let’s understand the definition of line,

A line is a one-dimensional shape that is straight, has no thickness, and can extend in both directions endlessly. It is commonly referred to as the shortest distance between two points.

Form of Equation of Line

The equation of a straight line on a two-dimensional coordinate plane can be represented in several ways in which the point-slope form, slope-intercept form, and standard form are most common.

Now let us understand all the three forms of the equation of a line;

• Point-slope form of the equation of a line: 

The point-slope form is derived from the concept of determining the slope of a given line. 

The Equation of a line in point-slope form is y-y1=m(x-x1),

where m is the slope of the line and (x1, y1) is the y-intercept.

• The standard form of the equation of the line:

The Equation of a line in standard form is Ax+By=C.

where, A, B, and C ≠0 are the real numbers and the value of A and B is not zero simultaneously. So, we can say that an equation of the form Ax + By + C = 0 is called the standard form of the Equation of a line.

where A, B, C are the Constants.

• The slope-intercept form of the equation of a line:

In slope-intercept form, a line’s equation is y=mx+c, where m is the line’s slope and b is the y-intercept.

Equation of a horizontal and vertical line

In a 2D Cartesian Plane, there are two axes, one is X-axis and another one is Y-axis. The line which is parallel to the x-axis is known as the Horizontal line and the line which are parallel to the y-axis is known as the vertical axis. 

Let’s us understand more about Equations of horizontal and vertical lines;

The equations of vertical and horizontal lines do not need any of the specific formulas. 

• A vertical line’s equation can be represented as X=c.

Where c is the constant and slope of a vertical line is not defined(undefine).

• A horizontal line’s equation can be represented as Y=c.

Where c is the constant and the slope of a horizontal line is zero (0).

Conclusion

Line: It is defined as a straight 1-D figure that has no thickness and extends indefinitely in both directions. 

• The slope of the Vertical line is not defined,
• The slope of a horizontal line is zero.
• Equation of line in point-slope form: y-y1=m(x-x1),

where m is the slope of the given line and (x1, y1) is the y-intercept

• Equation of line in slope-intercept form: y=mx+c

where m is the slope of the given line and b is the y-intercept

• Equation of a line in standard form: Ax+By=C

where, A, B, and C ≠0 are the real numbers