# 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

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:

$$y=mx+b,$$

where:

- $$$y$$$ 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

$$m=\frac{y_2-y_1}{x_2-x_1}$$For example, if we have the points $$$(2,3)$$$ and (4,7)$$$, the slope is

$$m=\frac{7-3}{4-2}=\frac{4}{2}=2$$**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.

### FAQ

#### 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.