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**Table of Content**

Use this slope calculator and let it find the slope (m) or gradient between two points \(A\left(x_1, y_1\right)\) and \(B\left(x_2, y_2\right)\) in the Cartesian coordinate plane.

Also, you can use the slope finder to calculate the following parameters:

- Slope intercept form
- Grade, distance, and angle
- 𝚫Y and X−coordinates
- Slope graph
- The x-intercept
- The y-intercept

**“The slope or gradient of the line is said to be a number that defines both the direction and steepness, ****incline**** or grade of line.”**

Typically, it is denoted by the letter (**m**) and is mostly known as rise over run.

Calculate slope by using the following formula:

**\(\ Slope \left(m\right)=\tan\theta = \dfrac {y_2 – y_1} {x_2 – x_1}\)**

Where

- \(\ m\ is\ the\ slope\)
- \(\theta\ is\ angle\ of\ incline\)

There are four types of slopes depending on the relationship between the two variables (x and y), which are:

- Positive
- Negative
- Zero
- Undefined

In the following slope table we have defined the types for a good understanding:

Positive |
Negative |
Zero |
Undefined |

The line increases from left to right side | Decreasing from left to right side | The rise of a horizontal line is zero | In this case, the Vertical lines do not move in any direction |

To find the slope, use this formula:

\(\ Slope \left(m\right)=\tan\theta = \dfrac {y_2 – y_1} {x_2 – x_1}\)

Also, you can use slope of a line formula to make instant calculations:

\(\ y =\ mx + \ b\)

You can expand the above formula to get the line equations in the point slope form:

\(\ y – y_{1} =\ m\ (x – x1)\)

There are two points are given: (2, 1) and (4, 7). We need to find the slope of the line passing through the points, the distance between points, and the angle of inclination.

**Solution:**

Given that:

- \(\ x_{1} = 2\)
- \(\ y_{1} = 1\)
- \(\ x_{2} = 4\)
- \(\ y_{2} = 7\)

Put the above values into the slope equation:

\(\ m =\dfrac {y_2 – y_1}{x_2 – x_1} =\dfrac {7 – 1} {4 – 2} =\dfrac {6}{2} = 3\)

**Distance Between Two Points:**

Use the Pythagorean theorem to find the distance between the points:

\(\ d = \sqrt{{(x_2 – x_1)^2 + (y_2 – y_1)^2}}\)

Substituting the coordinates (2, 1) and (4, 7):

\(\ d = \sqrt{{(4 – 2)^2 + (7 – 1)^2}} = \sqrt{{2^2 + 6^2}} = \sqrt{{4 + 36}} = \sqrt{40} \)

**Angle of Inclination:**

\(\ \tan(\theta) = \dfrac{{y_2 – y_1}}{{x_2 – x_1}}\)

Put the values of coordinates (2, 1) and (4, 7) in the equation above:

\(\ \tan(\theta) = \dfrac{{7 – 1}}{{4 – 2}} = \dfrac{6}{2} = 3 \)

Taking the arctangent (\(\arctan\)) of both sides:

\(\theta = \arctan(3) = 71.56 \ deg\)

The three ways to calculate slope are:

- Point slope form
- Slope-intercept form
- The standard form

Take the tangent of the angle:

\(\ m =\ tan\theta\)

Other Languages: Steigung Berechnen, 勾配計算, Calcul Pente, Calculo De Inclinação, Calcular Pendiente, Calcolo Pendenza, Калькулятор Уклонов, Výpočet Sklonu, Kattokaltevuus Laskuri, Eğim Hesaplama, Kalkulator Nachylenia, Kalkulator Kemiringan.