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# Slope Calculator

Add the known points of a line and let this online tool find the slope.

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
• 𝚫Y and X−coordinates
• Slope graph
• The x-intercept
• The y-intercept

## What Is Slope?

“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.

## Slope Formula:

Calculate slope by using the following formula: $$\ Slope \left(m\right)=\tan\theta = \dfrac {y_2 – y_1} {x_2 – x_1}$$ Where
• $$\ m\ is\ the\ slope$$
• $$\theta\ is\ angle\ of\ incline$$

## What Are The 4 Different Types of Slopes?

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

## How To Find Slope of A Line?

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: $$\ y - y_{1} =\ m\ (x - x1)$$

### Example:

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

### What Are 3 Ways To Find Slope?

The three ways to calculate slope are:
• Point slope form
• Slope-intercept form

### How Do You Convert An Angle To A Slope?

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.