Line Equation from Two Points Calculator

Introduction to Line Equation from two Points Calculator:

Line equation from two points calculator with steps is an online tool that helps you to evaluate the straight line equation from the given distinct points. It is used to simplify the process of finding the equation of the line that passes through between two points on the curve.

If you want a reliable tool that can find equation of line with two points problem quickly. Then equation of a line with two points calculator is the best tool you could ever find as it not only gives you the correct answers but also keeps you away from complex manual calculations.

What is an Equation of the Line with two Points?

Line equation two points is a process used to find the equation of a straight line that passes through between these two points on a graph in algebra. It satisfies each point on the line of the equation.

The line equation is used in various applications, such as graphing, predicting values, or solving geometric problems but It is also used in physics, engineering, and data analysis to analyze graphing systems.

Formula of Line Equation from Two Points:

The formula of the equation of line with two points consists of a slope of m that is found from the given two distinct points (x_1,y_1) and (x_2,y_2). The formula of equation of a line with two points used by line equation from two points calculator 3d is,

$$ y - y_1 \;=\; \frac{y_2 - y_1}{x_2 - x_1}(x - x_1) $$

How to Calculate Line Equation from Two Points?

For the calculation of the equation of line with two points, the line equation calculator from points follows some basic rules for solving the equations. Here is the guide for finding the line equation in different forms from point-slope form to standard form.

Step 1:

Identify the two given points be (x1, y1) and (x2, y2).

Step 2:

To Calculate the Slope m of the line use the formula of slope of the line which is given as,

$$ m \;=\; \frac{y_2 - y_1}{x_2 - x_1} $$

Step 3:

Put the value in the above equation to get the value of slope m to find an equation of a line with two points.

Step 4:

For the equation of a straight line use the Point-Slope Form formula which is given as:

$$ y - y_1 \;=\; m(x - x_1) $$

Step 5:

Add the value of slope m and the given points (x_1, y_1) into the point-slope form.

Step 6:

Simplify the above algebraic expression (if needed) to convert the line equation into a standard form that is given as,

$$ Ax + By \;=\; C $$

Solved example of Line Equation from Two Points:

The line equation from two points calculator with steps can find equation of line with two points easily but its essential for you to understand the step by step calculation process. So, an example is given below,

Example: Find an equation of a line with two points (-3, -1) and (2, -2)

Solution:

The given points (x1,y1) and (x2,y2) is,

$$ points\; (-3, -1)\;and\; (2, -2) $$

The equation of line for two points is,

$$ m \;=\; \frac{y_2 - y_1}{x_2 - x_1} $$

Put these points value in the above formula to find the value of m,

$$ m \;=\; \frac{-2 - (-1)}{2 - (-3)} $$

Solve it to get the value of m,

$$ m \;=\; \frac{-1}{5} $$

For the equation of the line that pass through between these points is,

$$ y - y_1 \;=\; m(x - x_1) $$

Put the value of x1 and y1 from the given equation (you can take other point as x1 and y1),

$$ x_1 \;=\; -3\; and\; y_1 \;=\; -1 $$

$$ y - (-1) \;=\; -\frac{1}{5} (x - (-3) $$

$$ y + 1 \;=\; -\frac{1}{5}(x + 3) $$

$$ y + 1 \;=\; -\frac{1}{5} x - \frac{3}{5} $$

$$ y \;=\; -\frac{1}{5}x - \frac{3}{5} -1 $$

After solving you get the solution of equation of line from two points,

$$ y \;=\; -\frac{1}{5}x - \frac{8}{5} $$

How to Use Line Equation from two Points Calculator?

The equation of a line with two points calculator has a simple design that enables you to find equation of line with two points easily and quickly.

Before the calculation process in the line equation calculator from points, you must follow some simple steps, so that you do not face any difficulty. These steps are:

1. Enter the value of the first point (x1,y1) for the equation of the line in its required input box.
2. Enter the value of the second point (x2,y2) for the equation of the line in the input box.
3. Review your points value before hitting the calculate button to start the evaluation process in the line equation from points calculator.
4. Click the “Calculate” button to get the result of your given equation from 2 points problem.
5. You should try out the line equation finder from points, if you have doubts about its solution then you can use the load example so that it provides you with an accurate solution.
6. Click on the “Recalculate” button to get a refresh page for the evaluation of more solutions of two points equation line questions.

Results of Equation of a Line with two Points Calculator:

Line equation from two points Calculator 3d gives you the solution as per the given questions when you add the input value in it. It may contain as:

• Result Option:

Result option of line between two points calculator gives you a solution for the equation of a line with two points problem to get the equation of a straight line in the solution.

• Possible Steps:

It provides you with a solution where all the evaluation processes are mentioned in a stepwise method for equation from 2 points problem.

Advantages of Using Line Equation Calculator from Points:

The equation of line from two points calculator provides many advantages whenever you use it to find the line equation from two points questions to get solutions immediately. These advantages are:

• The line between two points calculator is a handy tool that allows you to get the solution to different kinds of point for the line equation questions solution.
• Our line equation finder from points gives you benefits as you can use it to get solutions of more examples related to this concept.
• It is a free tool so that you can use it to find the line equation from two points question in real-time without spending any fee.
• The line equation from points calculator provides you with the solution in a complete process in a stepwise method so that you get clarity on equation of the line with two points method.
• Our tool saves you time and effort from doing equation of line from two points question calculations and provides the solution as per your given input question.
• Line Equation from Two Points Calculator with steps is easy to use tool so you can use it anywhere through any electronic device.