This Slope Calculator gives you the slope or gradient between two points of interest in the Cartesian coordinate system. Through this post you will learn what slope is, how to calculate it, slope of a line, formula and how to use this slope calculator.

## What is a slope in math?

In mathematics, a slope or gradient line is a number that describes both the direction and steepness of a line. We denote it frequently by m. This notation is use and appears at the earliest in England in 1844 when the Irish mathematician Matthew O’Brien wrote the straight-line equation as:

y = mx + b

## Slope Definition

The slope of a line in the plane containing the x and y axes is generally represented by the letter m. We define it as the change in the y coordinate divided by the corresponding change in the x coordinate between two distinct points on the line. The following equation describes this:

m= \frac{\Delta_y}{\Delta_x} = \frac {vertical \,change}{horizontal \,change} = \frac {rise}{run}

The delta symbol has the standard meaning of “change” or “difference” in mathematics.

## How to calculate slope?

We calculate the slope by finding the vertical change to the horizontal difference between any two points on the same line. A descending line has a negative rise. We use a “-” (minus) sign for it. The absolute value of its measures the steepness or grade lines. The line direction can be either increasing, decreasing, horizontal or vertical.

• A-line increases if it goes up from left to right. The slope is positive, m>0.
• A line decreases if it goes down from left to right. The slope is negative, i.e., m<0.
• If a line is horizontal, the slope is zero. This is a constant function.
• If a line is vertical, it is undefined.

Here the slope of the road between the two points is described as the ratio of the altitude change to the horizontal distance between any two points on the line.

In mathematical language, the slope m of the line is:

m = \frac {y_2 - y_1} {x_2 - x_1}

## The slope of a line

The slope of a line characterizes its direction. To calculate the slope, divide the difference between the y-coordinates of two points on a line by the difference between their x-coordinates.

### How to calculate the slope of a line?

We calculate the slope of a line simply by hand using absolute number coordinates. The formula becomes increasingly valuable as the coordinates take on larger values or decimal values. The concept of the slope is applying directly in grades or (gradients), geography, and civil engineering. In trigonometry, the slope m of a line is related to its angle incline theta tangent function.

m = \tan\theta

As a generalization of this practical description, the mathematics of differential calculus defines the slope of a curve at a point as the slope of the tangent line at that point. A curve is an object similar to a line but may not be straight. Learn more about trigonometric functions with this Cofunction Calculator.

## How to calculate slope with two points?

To determine the slope of a line given the coordinates of two points on the line, use the slope formula given below. The formula presents the change in y values divided by the change in x values. The first point’s coordinates indicate x1 and y1. The second point’s coordinates are x2, y2.

### The slope formula

Formula for slope calculation is given below:

Slope = \frac {y_2-y_1} {x_2 - x_1}

Where y and x represent the coordinate of two points used to calculate the slope between them. Our Slope Calculator is based on this formula.

## How to calculate slope percentage?

Percent of the slope is calculated by dividing the amount of elevation change by the horizontal distance travelled (also known as “the climb divided by the run”) and multiplying the result by 100.

## Slope intercept form

The slope-intercept form is the first of the linear equation forms. Slope-intercept equations are written as:

y=mx+b

where m is the slope of the line and b is the y-intercept of the line or the y-coordinate of the point at which the line crosses the y-axis.

## Point slope form

For linear equations, the generic form is used:

y-y_1 = m  (x-x_1)

It accentuates the line’s slope and a point on the line (that is not the y-intercept).