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x₁

y₁

x₂

y₂

Slope (m)

Angle (θ)

deg

Distance

Δx

Δy

The slope calculator determines the slope or gradient between two points in the Cartesian coordinate system. The slope is basically the amount of slant a line has and can take on positive, negative, zero or an undefined value. Before we can use the calculator we might want to learn how to find the slope using the slope formula. To find the equation of a line for any given two points that this line passes through, use our slope intercept form calculator.## How to find slope

## The slope formula

## Other related topics

- Identify
`(x₁,y₁)`

and`(x₂,y₂)`

. We will use the formula to calculate the slope of the line passing through the points`(3,8)`

and`(-2, 10)`

. - Input the values into the formula. This gives us
`(10 - 8)/(-2 - 3)`

. - Subtract the values in parentheses to get
`2/(-5)`

. - Simplify the fraction to get the slope of
`-2/5`

. - Check your result using the slope calculator.

To find the slope of a line we need two coordinates on the line. Any two coordinates will suffice. We are basically measuring the amount of change of the y-coordinate, often known as the *rise*, divided by the change of the x-coordinate, known the the *run*. The calculations in finding the slope are simple and involves nothing more than basic subtraction and division.

`slope = (y₂ - y₁) / (x₂ - x₁)`

Notice that the slope of a line is easily calculated by hand using small, whole number coordinates. The formula becomes increasingly useful as the coordinates take on larger values or decimal values.

It is worth mentioning that any horizontal line has a gradient of zero because a horizontal line has the same y-coordinates. This will result in a zero in the numerator of the slope formula. On the other hand, a vertical line will have an undefined slope since the x-coordinates will always be the same. This will result a division by zero error when using the formula.

Just as slope can be calculated using the endpoints of segment, the midpoint can also be calculated. The midpoint is an important concept in geometry, particularly in applications such as inscribing a polygon inside another polygon with the vertices touching the midpoint of the sides. This can be obtained using the midpoint calculator or by simply taking the average of each x-coordinates and the average of the y-coordinates to form a new coordinate.

The slopes of lines are important in determining whether or not a triangle is a right triangle. If any two sides of a triangle have slopes that multiply to equal -1, then the triangle is a right triangle. The computations for this can be done by hand or by using the right triangle calculator. The the distance calculator will compute which side or a triangle is the longest, which helps determine which sides must form a right angle if the triangle is right.