How to calculate the slope of a line

A key concept in mathematics and economics is something called slope. We can find it in the representation of the equations and determine the inclination of the line with respect to the coordinate axes. In this article, you will understand its importance, use, and how to calculate the slope of a line .

What is a slope?

In short, the slope is a numerical calculation that indicates whether a line moves up or down. And how steep is the line.

Now in the economy, the understanding of the slope and how the line looks is very important. This is so because to help make material and concepts easier to understand, we use images and graphics.

So, basically the slope tells you if a line moves up or down and the degree of inclination that slope has. So think of this as a hill. The slope will tell you if you are going up a hill or going down it. And how is that hill of steep.

How do we use the slope?

The next step is to understand how the slope is used and why it is important to calculate it. As I just mentioned, it tells you if a line moves up or down and the degree of tilt it has.

By looking at the value of the slope, you can immediately tell if that line goes up or down. How?.

  • If the slope is a positive number, then the line moves up.
  • If the slope is a negative number, then the line moves down.

And the larger that number is, the more inclined the line is.

So a slope of 4 means that the line goes up. But a slope of -4 means that the line moves down. And a line with a slope of 3 is steeper than the line with a slope of 2.

Part 1

The lines are composed of individual points. And each point has a value of the X axis and a value of the Y axis. The X axis is horizontal (left and right) and the Y axis is vertical (bottom to top).

For example, (3, 5). This means that we have a value of the X axis of 3 and a value of the Y axis of 5. And that tells us that this point is 3 on the right and 5 on the top.

The point (1, 6) is 1 on the right and 6 on the top. So think of the points as street addresses. The lines would be a whole street with lots of houses (points).

Part 2

Well, we've finally reached the point where you can really start working with the numbers to get the value of the slope .

We take two points, look at them, and see how much space there is between the two Y axes.

For example, suppose we have points (1, 2) and (3, 5). Our two values ​​of the Y axis are 2 and 5. Remember, the values ​​of the Y axis are the numbers on the right, the values ​​of the X axis are the numbers on the left.

How far are the 2 points of Y ?. Simple, subtract 5-2 = 3 We call the result, Elevation .

Part 3

Our next step is to get the distance between our X-axis values. This difference is called Advance .

Continuing with our previous example, we look at our two points (1, 2) and (3, 5) to see what the values ​​of the X axis are. Here we have 1 and 3.

And just as we did when the Elevation was calculated, we subtract. 3-1 = 2 this gives us our Advance .

So:

  • Elevation is the difference between the two Y axes
  • Advance is the difference between the two X axes

Part 4

This is our last step to calculate the slope of a line .

All we do is divide the Elevation by Advance . Using the example, divide 3 by 2, which gives us a slope of 1.5.

And what does this tell you?

  • We know that our line moves up because the slope is positive.
  • We know that it is a steeper slope than a straight with the slope of 1. However, it is not as steep as a slope of 2.

Slope formula

This is the mathematical formula to calculate the slope, given two points.