Study Tips- An Easy Approach to Finding the Equation of a Line with One Point

In math and physics, there are several situations in which you would need to consider the equation of a line. It plays a significant role in chemistry as well, you’ll find linear equations in gas analyses, when measuring reaction rates, and when determining Beer’s Law. Here is a brief description and an illustration of how (x, y) data can calculate the equation of a line.

There are various types of line equations including the regular form, point-slope form, and slope-line form of intercept. The point-slope or slope-intercept forms are both appropriate choices if you are asked to find the equation of a line and not specified which type to use.

Below is the easy approach for finding the equation of a line with one point that is also known as point slop.

Equation of a line

Equation of a line has a standard Form that is written as

y = mx+ c

Here, m represents the slope and c represents the y-intercept. The y-intercept can also be expressed as the point (0, b). It is one of the simplest ways to express the equation of a line.

Point-Slope Form of the Equation of a Line

When you write the standard form of the equation of a line in terms of the point-slope form, this equation of a line (y = mx + c) holds slope m and moves through the point (x1, y1).

Then the equation in point-slope form is written as:

y – y1 = m (x – x1)

where m represents again the slope of the line and (x1, y1) are the coordinates of the given points.

thus, from the equation above it is clear that the point-slope form can be determined by finding the difference among two points (y-y1) in y-coordinate and x-coordinate points (x-x1) on a line is proportional to each other.

Why is it impossible to determine the equation of the line with one point only?

It is because, with the aid of only one point, it is not possible to find the equation of a line, the reason is that the countless numbers of lines can cross through any point. Thus, it’s only necessary to find a line equation with one point if at least one additional parameter, such as the line slope, is also provided.

Finding out the equation of a line with one point

The equation of a line with one point can easily be calculated by using the point-slope formula mentioned above. Below are the key steps you must follow to determine the point-slope form manually.

  • Start by writing the values of x1, y1, and slope
  • The next step is stating the formula for point-slope.
  • Insert the values in the formula and evaluate the line equation.

Solved example

Now, for finding the point slop, there is a must to have the values of one point along with the slope so that you would easily calculate the equation of the straight line with one point.

According to the equation, (X1, Y1) refers to as one point and the M refers to as the slope .

Y -Y1= M (X-X1)

This above equation shows the equation of the straight line passing through a point and the slope as well.

Let’s solve a question now

Question: when the point 2, 3 builds an angle of 45° on positive X-axis, then determine the line of the equation of the straight line through these points.

In the question above you are provided with a point that is (2,3) but the slope is not given.

Here we will first find out the slope by simply using the relationship between the angle and the slope, that refers to as M =

tan A (A = angle)
M = tan45°
M = 1

Thus, 1 is the slope

Now write down the formula and put the values in it.
Y -Y1= M (X-X1)
Y -3 = 1 (X -2)
Y-3 = X-2

Thus, this line of equation will be a straight line.

Point slope calculator

The other simple way of finding the point-slope form is by using the online point-slope formula calculator. The point-slope forms calculator is an automated strategy for identifying the basic line equation as Ax + By + C = 0. To calculate the line of equation by using a calculator, all it requires is a slope m and a point A (x1, y1) coordinates. The point-slope calculator is an efficient service that allows the line slope to be measured in no time.

Meracalculator offers you an efficient and easy to use online point-slope calculator for free of cost. It is very simple to use, below we are discussing how to use this calculator. This calculator helps you to find out the point-slope form equation and the equation of the line in no time.

How to use the point slope form calculator from?

The interface of point slope equation calculator is straightforward, and it is the reason the calculator user friendly and uncomplicated. It is a tool that is not restricted only to students. Anyone who has to deal with subjects like math, physics, and chemistry can access it easily. Thus, it becomes helpful for teachers, engineers, computer graphics experts, aeronautical staff, etc. Below are the steps that you must follow to use its services.

  • First, the coordinate for X1 is inserted in the provides input field.
  • Then the coordinate for Y1 is inserted in the second input field.
  • Then insert the coefficient of slope m in the respective filed for slope.
  • Tap the Calculate button below after making sure of entering all values correctly. The result will be on your display immediately.
  • New values can be entered, once the calculation has completed by hitting the Reset button.

The given fields must be filled to find out the equation of the straight line without a hitch. It is a great tool that can not only assist in calculating the equation of the line with a single point but also help in making the line on a Cartesian plane that can be helpful for some extra explanation.