**How to Find point-slope Form from two points**: What is Point-slope form? Point-Slope form, Two-Point slope form, Slope-Intercept form, Intercept form. Understanding different forms of linear equations is essential in mathematics and plays a crucial role in various real-world applications. One of the widely used forms is the point-slope form. In this article, we will delve into the concept of point-slope form and learn how to find the equation of a line using two given points. With clear explanations and illustrative examples, you’ll soon master this fundamental skill.

## What is Point-slope form?

There are several methods to find the equation of a straight line. The technique chosen to solve a problem depends on the data provided. Some commonly used methods are:

- Point-Slope form
- Two-Point slope form
- Slope-Intercept form
- Intercept form

## Exploring Point-Slope Form:

Point-slope form is expressed as y – y₁ = m(x – x₁), where (x₁, y₁) represents a point on the line and ‘m’ represents the slope of the line. To find the equation of a line using two given points, we follow a simple three-step process.

### Step 1:

Calculate the Slope (m): The slope (m) can be determined by using the formula: m = (y₂ – y₁) / (x₂ – x₁)

### Step 2:

Select a Point (x₁, y₁): Choose one of the given points to serve as (x₁, y₁) in the point-slope form equation.

### Step 3:

Substitute Values and Simplify: Substitute the values of (x₁, y₁), (x₂, y₂), and the calculated slope (m) into the point-slope form equation. Then, simplify the equation to obtain the final result.

## Important Examples: How to Find point-slope Form from two points

Here we are going to write the important examples

### Example 1:

Let’s find the equation of a line passing through the points (2, 4) and (5, 9).

Step 1: Calculate the Slope (m): m = (9 – 4) / (5 – 2) m = 5 / 3

Stp 2: Select a Point (x₁, y₁): Let’s choose (2, 4) as our reference point.

Step 3: Substitute Values and Simplify: Using the point-slope form equation, we have: y – 4 = (5/3)(x – 2)

Expanding the equation: 3y – 12 = 5x – 10

Rearranging the terms to obtain the standard form: 5x – 3y = -2

Thus, the equation of the line passing through (2, 4) and (5, 9) is 5x – 3y = -2.

### Example 2:

Consider the points (-3, 7) and (1, -1). Let’s find the equation of the line using the point-slope form.

Step 1: Calculate the Slope (m): m = (-1 – 7) / (1 – (-3)) m = -8 / 4 m = -2

Stp 2: Select a Point (x₁, y₁): We’ll select (-3, 7) as our reference point.

Step 3: Substitute Values and Simplify: Using the point-slope form equation, we have: y – 7 = -2(x – (-3))

Simplifying the equation: y – 7 = -2(x + 3)

Expanding further: y – 7 = -2x – 6

Rearranging the terms to obtain the standard form: 2x + y = 1

Hence, the equation of the line passing through (-3, 7) and (1, -1) is 2x + y = 1.

## Facts point-slope Form from two points

concept of point-slope form is crucial in understanding linear equations. By following the step-by-step process of finding the equation of a line from two given points.

## Important Examples of Find Slop of Two Points

Example 1: Let’s find the equation of a line passing through the points (3, 5) and (-2, -4).

Step 1: Calculate the Slope (m): m = (-4 – 5) / (-2 – 3) m = -9 / -5 m = 9/5

Stp 2: Select a Point (x₁, y₁): We’ll choose (3, 5) as our reference point.

Step 3: Substitute Values and Simplify: Using the point-slope form equation, we have: y – 5 = (9/5)(x – 3)

Expanding the equation: 5y – 25 = 9x – 27

Rearranging the terms to obtain the standard form: 9x – 5y = -2

Therefore, the equation of the line passing through (3, 5) and (-2, -4) is 9x – 5y = -2.

### Explanation:

In this example, we first calculate the slope (m) using the formula, which gives us the value 9/5. Then, we select one of the given points, (3, 5), as (x₁, y₁) in the point-slope form equation. By substituting the values into the equation and simplifying, we obtain the standard form equation of the line.

### Example 2:

Consider the points (-1, 2) and (4, 6). Let’s find the equation of the line using the point-slope form.

Step 1: Calculate the Slope (m): m = (6 – 2) / (4 – (-1)) m = 4 / 5

Stp 2: Select a Point (x₁, y₁): We’ll select (-1, 2) as our reference point.

Step 3: Substitute Values and Simplify: Using the point-slope form equation, we have: y – 2 = (4/5)(x – (-1))

Simplifying the equation: y – 2 = (4/5)(x + 1)

Expanding further: y – 2 = (4/5)x + 4/5

Rearranging the terms to obtain the standard form: 4x – 5y = -6/5

Hence, the equation of the line passing through (-1, 2) and (4, 6) is 4x – 5y = -6/5.

Explanation: In this example, we calculate the slope (m) using the given points, which gives us the value 4/5. We then select (-1, 2) as our reference point and substitute the values into the point-slope form equation. By simplifying and rearranging, we arrive at the standard form equation of the line.