Slope-Intercept Form Calculator with Two Points

Find the slope-intercept form of a line step by step

The slope-intercept form calculator will find the slope of the line passing through the two given points, its y-intercept, and the slope-intercept form of the line, with steps shown.

Related calculators: Line Calculator, Slope Calculator, Parallel and Perpendicular Line Calculator


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Discover our Slope Intercept Form calculator, specially designed to quickly deliver the slope-intercept equation using two points. In addition, this tool also shows basic information about the line. It is ideal for students, educators, or math fans.

How to Use the Slope-Intercept Form Calculator with Two Points?

  • Input

    Start by entering the coordinates of your first point into the designated fields. Repeat this step for your second point.

  • Calculation

    After ensuring your points are accurately inputted, click the "Calculate" button to initiate the computation process.

  • Result

    Once processed, the calculator will display the slope of the line formed by your two points, as well as the x-intercept, the y-intercept and the equation of the line.

What is the Slope Intercept Form?

The slope-intercept form is a special form of the equation of a straight line. It is one of the most commonly used linear equations because of its straightforwardness in expressing both the slope of the line and its y-intercept.

The slope-intercept form of the equation is given by the following formula:



  • $$$y$$$ is the dependent variable, typically representing the vertical coordinate.
  • $$$x$$$ is the independent variable, typically representing the horizontal coordinate.
  • $$$m$$$ is the slope of the line. It defines the rate of change of $$$y$$$ with respect to $$$x$$$. In geometric terms, the slope represents the rise over the run, or how much $$$y$$$ changes per unit change in $$$x$$$.
  • $$$b$$$ is the y-intercept. This is the point where the line crosses the y-axis. In simpler terms, it's the value of $$$y$$$ when $$$x$$$ is zero.

This equation provides valuable information about the line it represents:

  • Slope $$$(m)$$$: The slope measures how steep the line is. It is the "rise" over the "run", mathematically represented as the change in the $$$y$$$ over the change in the $$$x$$$.

    The formula for the slope, given two points $$$\left(x_1,y_1\right)$$$ and $$$\left(x_1,y_1\right)$$$ is


    For example, if we have the points $$$(2,3)$$$ and (4,7)$$$, the slope is

  • Y-intercept $$$(b)$$$: The y-intercept is where the line intersects (crosses) the y-axis. Mathematically, it's the value of $$$y$$$ when $$$x=0$$$. It is the point of the line on the vertical axis.

The slope-intercept form has a wide range of applications:

  • Economics: Used to visualize cost functions, revenue functions, or any linear relation between variables.
  • Physics: Helps to define relationships in linear motion or any scenario where a direct linear relationship is observed.
  • Everyday Life: Can help to estimate budgets, predict outcomes, or calculate simple relations between two variables.

Why Choose Our Slope-Intercept Form Calculator with Two Points?

  • Precision and Accuracy

    Our calculator undergoes rigorous testing to ensure precise and accurate results. Whether you are dealing with simple coordinates or very complex ones, expect correct results every time.

  • User-Friendly Interface

    We prioritize a smooth user experience. The intuitive design ensures that anyone, from beginners to seasoned mathematicians, can navigate and use the tool efficiently.

  • Speed

    No more manual calculations or waiting. Get instant results, making it incredibly useful for quick checks, homework assistance, or real-time problem-solving.

  • Versatility

    Beyond just computing the slope and y-intercept, our calculator provides the point-slope form of the line, which increases its usefulness for various mathematical applications.


What is the slope-intercept form?

The slope-intercept form of a linear equation is $$$y=mx+b$$$, where $$$m$$$ denotes the slope of the line, and $$$b$$$ is the y-intercept. It's a way to describe a straight line on a two-dimensional plane using its slope and the point where it intersects the y-axis.

What if my points lie on a horizontal line?

For a horizontal line, the slope $$$m$$$ will be $$$0$$$. Your equation will be of the form $$$y=b$$$, where $$$b$$$ is the y-coordinate of your two points.

How can I visualize the line represented by the slope-intercept equation?

To visualize the line, plot the y-intercept on a graph and then use the slope to determine the rise and run. Alternatively, many online graphing tools allow you to input the equation and will display the line for you.

What's the difference between the slope-intercept form and point-slope form?

The slope-intercept form is given by $$$y=mx+b$$$, focusing on the slope and the y-intercept. The point-slope form is $$$y−y_0=m(x-x_0)$$$. It emphasizes the slope and the specific point $$$\left(x_0,y_0\right)$$$ on the line. Both are useful, but their applications might differ depending on the context.