October 30, 2022

The slope is the gradient of two given points on a line, usually on a Cartesian plane. Each point is given in terms of x and y coordinates. For instance, assuming the two points of a line, you would like to find the gradients are A and B. Then the points of A will be (x1, y1), and the points of B will be (x2, y2).

However, a slope calculator will help you conveniently find the gradient of any line by just inputting the x and y coordinates and clicking the calculate button. The general formula for finding the slope of a line is (y2-y1)/ (x2-x1). Here is everything you need to know about a slope calculator.

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What Is a Slope Formula?

The slope formula determines the steepness of a line or how the line is inclined. To find the slope of a line, you must have the x and y coordinates of any given two points on a straight line. Although you can also find the gradient of a curved line, it is not uniform for all the points on the line.

The gradient of a line can also be defined as the ratio of change in the y-axis to the ratio of change in the x-axis on a Cartesian plane. It is the change in y coordinates with respect to the change in x coordinates. The slope formula is expressed as m = (y2 – y1)/ (x2 – x1) = Δy/Δx where y1 and y2 are the coordinates on the y-axis while x1 and x2 are the coordinates on the x-axis.

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M is the gradient of the line, and Δ is the symbol for change. However, all these formulas are incorporated into an online slope calculator. All you have to do is to input the x and y coordinates and then click the calculate button.

How Slope Formula Is Derived

When calculating the slope of a line, the x and y coordinates are used. The net change in x coordinates is denoted by Δx, while Δy denotes the net change in y coordinates. Therefore, the changes in y coordinates with respect to x coordinates are expressed as Δy/Δx, and the slope is denoted by m; therefore, m = Δy/Δx.

Also, drawing a straight line through the origin on a Cartesian plane will make a right-angle triangle whose angle θ is given by height/base. Now from trigonometric ratios, we know that height/base = tanθ. Therefore slope formula can also be expressed as m = tanθ which equals Δy/Δx. Therefore, m = tanθ = Δy/Δx = (y2 – y1)/ (x2 – x1).

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The Slope Equation

We have already discussed the slope formula and how to derive it using a straight line passing through the origin on a Cartesian plane or a line that cuts the y-axis at point 0. However, you can also find the gradient of a line given the y and x intercepts or where the line crosses the x and y-axis. The straight line equation is expressed as Y = MX + C, where C is the y-axis intercept and m is the gradient.

Summary

A slope calculator is used to find the gradient of a line by just inputting the x and y coordinates of the line. One thing you need to know about the slope of a line is the slope formula and how to derive it. You should also know how to derive, interpret and use the slope equation in solving various math problems involving a straight line.

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