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
- ?Y 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.
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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: \(\theta = \arctan(3) = 71.56 \ deg\)
FAQ’s:
What Are 3 Ways To Find Slope?
The three ways to calculate slope are:
How Do You Convert An Angle To A Slope?
Take the tangent of the angle: \(\ m =\ tan\theta\)
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