Coordinate Geometry: The Most Widely Used Branch of Mathematics

Coordinate geometry is one of the biggest and most used branches of mathematics. This branch of mathematics deals with Coordinate planes and different points which lie on the plane. This geometry is usually taught to students of the higher secondary classes and for the students who want to pursue their career as an engineer, this topic is a must. This branch of mathematics has a wide range of applications to be used in everyday life. This beautiful branch of geometry deals with lines, slopes, different curves, and many other things. In this branch students also study to take out the slope of any line with the help of the slope intercept form of the line, the point slope form of the line, etc.

This article deals with different types of methods to take out the slope of any line.

Some of them are:

  • Point slope form
  • Slope intercept form
  • Two-point form

First of all, let’s discuss the meaning of the slope of any line.

In simple words, a Slope can be defined as the change in the y-axis divided by the x-axis.

Two-point form:

The two-point form is applied to determine the equation of a line in the coordinate plane. The equation of any line can be easily taken out through different methods based on the information which is provided. The two-point form is one of the widely important forms which is used to present a straight line algebraically.

The slope of these lines can be expressed with the help of the difference of the y-axis that is divided by the x-axis.

Apply the two-point formula given as

y-y1 = (y2−y1/x2−x1)(x−x1) where the slope of the line is taken by the difference between two Coordinates.

Slope intercept form:

The slope-intercept form that is used in a straight line is undoubtedly one of the most widely used forms used to represent the equation of a line. The slope-intercept formula is used to determine the equation of a line when the slope of the straight line is given and the y-intercept(the y-coordinate of that point where the line cuts the y-axis). The equation of a line is taken out by satisfying each point that lies on that respective line.

The slope-intercept form is a way used to give the equation of a straight line in the coordinate axis. The equation of a straight line will be checked by the:

  • the coordinates of any point on the line should satisfy.
  • the coordinates of that point which will not satisfy the line.

The best thing about this equation is that it is straightforward. To find out the slope-intercept form of any straight line, one would need the slope of the line or the angle on which the line is inclined or tilted from the Coordinate axis.

Using the give slope-intercept formula, the equation of the line will be as follows:

y = mx + c


c is the intercept which is made on the y-axis and m is the slope of the line which is given.

(x, y) will satisfy every point on the line. x and y should be used as the variables while using the formula used above

Point slope form of a line:

Point slope form is used to present a straight line using its slope and a point on the given line. That means the equation of a line whose slope is in the form of ‘m’ and which will pass through a point can be found by the point-slope form.  This form of the line can only be used when one knows the slope of the line.

y − y1 = m (x − x1), this is the equation that is used to find the required line with the help of point-slope form. Y and X are fixed whereas x1 and y1 are to be taken as variables.

These are some of the basic forms which we study in mathematics.

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