# Slope Calculator

The slope calculator determines the slope or gradient between two points in the Cartesian coordinate system.

The slope calculator determines the slope or gradient between two points in the Cartesian coordinate system.

- Identify the coordinates
`(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 the division by zero error when using the formula.