# Point Slope Form Calculator + Online Solver With Free Steps

The online **Point Slope Form Calculator** is a calculator that allows you to represent a straight line in a **linear equation** form.

The **Point Slope Form Calculator** is a powerful tool that helps mathematicians and scientists to find the point-slope form of a line.

## What Is a Point Slope Form Calculator?

**A Point Slope Form Calculator is an online tool that helps you determine the point-slope form of a calculator of a straight line.**

The **Point** **Slope Form Calculator** requires two inputs: the value of the slope and the points the line passes. Using the inputs, the **Point Slope Form Calculator** quickly calculates the point slope from the line.

## How To Use a Point Slope Form Calculator?

To use the **Point Slope Form Calculator**, you will need to input the data of the line in their respective boxes and click the “Submit” button. The calculator will display the results in a new window.

The detailed instructions for using a **Point Slope Form Calculator** are given below:

### Step 1

First, we add the **value of the slope** into the **Point Slope Form Calculator**.

### Step 2

After adding the value of the slope, we add the **points where the line passes through** in the **Point Slope Calculator**.

### Step 3

Once we have entered both these inputs, we click the **“Submit”** button present on the **Point Slope Form Calculato**r. The calculator displays the point-slope form and a graph in a separate window.

## How Does a Point Slope Form Calculator Work?

The **Point Slope Form Calculator** works by taking in the inputs and turning the line equation into the point-slope form. The point-slope form is generally represented as the following equation:

**y – y1 = m ( x – x1 )**

## What Are Linear Equations?

A **linear equation** is an equation in which the variable’s maximum power is consistently 1; another name for this is a one-degree equation. A linear equation with one variable has the following standard form:

**Ax + B = C **

A is a coefficient, B is constant, and x is a variable in this situation. A **linear equation** is also known as a **linear equation** because it always produces a straight line when all possible solutions are graphed.

It makes no difference if you use whole integers, fractions, decimals, etc., for the x and y values. Each answer pair is on the graphed line. Nearly every part of life can benefit from using **linear equations**.

Examples include computing distance, calculating hourly pay, figuring out how much to charge in banking and engineering, and calculating how much medication to administer to a patient based on their weight and age.

A linear equation for a graph is usually represented by:

**y = mx + c **

## Point Slope Form

The **point-slope form** calculates the equation of a straight line inclined to the x-axis at a certain angle and passes through a particular point. The equation of a line is an equation that is satisfied by every point on the line. This indicates that a **linear equation **with two variables represents a line.

Multiple methods are used to find the equation of a line depending on the information given. When we know the slope of a line and a point on it, we may utilize the **point-slope** formula.

The **point-slope form** expresses a straight line by using its slope and a point on the line. The equation of a line with slope m and passing through a point (x1, y1) is determined using the** point-slope form**.

### Formula for Point Slope Form

The **point-slope form** **formula** is used to calculate the equation of a line. The point-slope form is used to calculate the equation of a line with a specified slope and a given point.

This formula is only utilized when the slope of the line and a point on the line are known. Other formulas for determining the equation of a line include slope-intercept form, intercept form, and so on. The **point-slope formula** is as follows:

**y – y1 = m ( x – x1 ) **

Where:

**Random point on line = (x,y) **

**Fixed point on the line = (x1, y1) **

**m = Slope of the line **

### Deriving the Point Slope Form Formula

The **point-slope formula** is derived using the equation for the slope of the line. Consider a line with slope m. Assume that (x1, y1) is a known point on the line. Let (x, y) be any other random point on the line with unknown coordinates.

We know that the equation for a line’s slope is:

\[ m = \frac{(y-y_{1})}{(x-x_{1})}\]

We multiply (x- x1) on both sides and get:

**m(x – x1) = (y – y1) **

Which can be written as:

**y – y1 = m ( x – x1 ) **

Hence this **derivation** proves the formula.

## Solved Examples

The **Point Slope Form Calculator **instantly allows you to find the point-slope form of a linear graph.

The following are some examples solved using the **Point Slope Form Calculator**:

### Solution

Using the **Point Slope Form Calculator**, we can easily find the point-slope form of the graph. Initially, we enter the value of the slope into the **Point Slope Form Calculator**; the value of the slope is 4. After entering the slope value, we enter the point where the line passes through in our calculator; the point where the line passes through is (2,5).

After entering the slope’s value and the point where the line passes through in their respective boxes, we click the **“Submit”** button on the **Point Slope Form Calculator**. The calculator immediately displays the results and plots the graph in a separate window.

The following results are extracted from the **Point Slope Form Calculator**:

Input Interpretation:

Line:

**Slope = 4 **

**Through = (2,5) Cartesian Plane **

Result:

**y = 4x – 3**

Visual Representation:

Properties of line:

**x intercept : $\frac{3}{4}$ = 0.75 **

**y intercept : -3 **

### Example 2

During an assignment, a college student came across a linear graph with a slope value of 3, and the line passed through the point (-1,2). To complete his assignment, the student had to find the point-slope form of the linear graph. With the help of the **Point Slope Form Calculator,** find the **point-slope form** of the linear graph.

### Solution

Using the **Point Slope Form Calculator**, we can quickly determine the graph’s point-slope form. First, we enter the slope value into the **Point Slope Form Calculator**; the slope value is 3. We input the point where the line passes through our calculator after entering the slope value; the point where the line goes through is (-1,2).

We press the **“Submit”** button on the **Point Slope Form Calculator** after entering the slope’s value and the point where the line passes through their corresponding boxes. The calculator displays the findings immediately and plots the graph in a separate window.

The **Point Slope Form Calculator** produced the following results:

Input Interpretation:

Line:

**Slope = 3**

**Through = (-1,2) Cartesian Plane **

Results:

**y = 3x + 5**

Visual Representation:

Properties of line:

**x intercept : – $\frac{5}{3}$ $\approx$ 1.66667**

**y intercept : 5**

### Example 3

A mathematician needs to find the point-slope form of a linear graph. The linear graph has a slope value of -5 and passes through the point (4,-3). Using the information provided, find the **point-slope form** of the linear graph.

### Solution

We can quickly determine the point-slope form of the graph using the **Point Slope Form Calculator.** First, we enter the slope’s value into the **Point Slope Form Calculator**; the value of the slope is -5. After entering the slope value, we enter the point where the line goes through into the **Point Slope Calculator**. The point where the line goes through is (4,-3).

The slope value and the point where the line intersects are entered into the corresponding fields on the Point Slope Form Calculator before clicking the **“Submit”** button. The **Point Slope Form Calculator** shows the results immediately, and a separate window is used to plot the graph.

The following results are generated using the **Point Slope Form Calculator**:

Input Interpretation:

Line:

**Slope = -5**

**Through = (4,-3) Cartesian Plane **

Results:

**y = 17 – 5x**

Visual Representation:

Properties of line:

**x intercept : – $\frac{17}{5}$ = 3.4 **

**y intercept : 17**

### Example 4

Consider the following values of a linear graph:

**Slope = 2 **

**Line passing through = (1,2) **

Use the information above to find the point-slope form of the linear graph.

### Solution

We can easily find the point-slope form using the **Point Slope Form Calculator**. We add the information we are provided into their respective boxes in the **Point Slope Form Calculator**. Click the “Submit” button, and the calculator will generate the results.

The following results are generated from the **Point Slope Form Calculator**:

Input Interpretation:

Line:

**Slope = 2**

**Through = (1,2) Cartesian Plane **

Results:

**y = 2x**

Visual Representation:

Properties of line:

**x intercept : 0 **

**y intercept : 0 **

*All images/graphs are made using GeoGebra.*