How To Work Out The Gradient Of A Line?

One of the popular terms in Mathematics and economics is called gradient. The gradient is also called the slope. The gradient shows the steepness and direction of a line.

The slope is referring to the x-y or rectangular coordinate system. The coordinate system helps to determine the direction referring to the origin.

In this article, we will describe the use and method to find the gradient.

X-Y Coordinate System

x-y coordinate system

In the x-y coordinate system, the horizontal line defines x-axis. The vertical line defines the y-axis. The point where both axis cuts each other is called origin.

Positive Gradient

Positive gradient

Referring to the origin the slope going up from left to right is called positive gradient. It also indicates the progress of work or profit. As the line moves up, the value of gradient would be positive.

Negative Gradient

Negative gradient

Referring to the origin the slope going down from left to right is called negative gradient. It also indicates the loss of work. As the line moves down, the value of gradient would be negative.

Rise and Run

run and rise

As the slope is the change in the line. If this change is on the vertical side then it is called rise and if it is on the horizontal side then it is called run.

Methods Of Calculating Gradient

Gradient can be calculated using 2 methods

  • Using changes across x and y-axis
  • Using polar coordinates

Now let’s discuss these methods one by one.

Calculation of gradient using changes across x and y-axis

changes across x-y axis

The green colored dotted line shows the change across y-axis and the purple colored line shows change across the x-axis.

The equation for the slope would be

m = change in y-axis / change in x-axis

“m” is the abbreviation for the slope.

example of calculating Gradient

In this figure, the change across the y-axis is 8 and across x-axis is 4. Now put these values

m = 8 / 4

m = 2

calculating gradient using changes in axis

In this figure, the change across the y-axis is 4 and across x-axis is also 4. By putting these values

m = 4/4

m = 1

From these examples, we can say that the steeper the line is greater the value of gradient would be.

Calculation of gradient using polar coordinates

polar coordinates

Polar coordinates are given in the bracket. The “,” sign separates the values, the value at the left side is for x-axis and the value at the left side is for the y-axis.

Slope has the same equation as that of above method.

m = change in y-axis / change in x-axis

or

m = y2-y1 / x2-x1example of calculating slope by polar coordinates

In this figure we have two polar coordinates and by putting them into the equation

m = 6-2 / 8-6

m = 4/2

m = 2

calculating negative slope by polar coordinates

In this figure, we have a negative slope and by putting its polar coordinates into the equation

m = 8-9 / 4-2

m = -1 / 2

m = -0.5

It is clear from the example, that the negative slope has the negative value of gradient.

I hope you liked my post about gradient and if you have any query or want to give suggestions you can write it down in the comments section.

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