# The slope: direction and steepness of a line.

## Meaning

The slope is a complicated and abstract concept, especially if you read or hear it for the first time. Moreover, the word is compound! Compound means that the word is "made" by sticking two words together; in this case 'direction' and 'coefficient' . Slope is easier to understand due to the meaning of the words, direction and coefficient. The word direction speaks for itself: “He went left or right”. The word coefficient is a bit trickier, it is an 'expensive' word for number. The term slope coefficient is therefore a number that says something about the **direction** and steepness of a line.

In addition to the term slope coefficient, the term 'slope number' is also used. But that is lead for scrap because this is a typical case of 'name dropping'.

## Role of slope in mathematics.

Just as Sint and Piet belong together, so in mathematics the slope belongs to the linear (line) relationship. The general formula of a linear relationship or line is: ƒ(x) = ax + b. By assigning a value to the letters a and b, for example a=3 and b= 7, you get a specific line: ƒ(x) = 3x + 7. The number that stands before the x, the number 3, is the slope of the line. As mentioned earlier, the slope is a number that gives information about the course or direction of the line. There are four types of lines: 1) ascending lines 2) descending lines 3) the horizontal line and finally 4) the vertical line. The figure below shows the four types of lines.

The horizontal line and the vertical lines speak for themselves. Ascent and descent needs some explanation. Just like you read from left to right, you also read and look at mathematics. The reading direction determines whether you call a line ascending or descending. If you "walk" from left to right and if you go up, the line is rising, the slope of the road goes up. One way to remember it is by drawing a man on the lines. You can see for yourself whether this man is walking down or up.

Now that you know when a line descends and rises, we can link that to the slope of the line. If a line rises, the slope is always a positive number, see figure below. If the slope is a negative number, the line drops. (A horizontal line has a slope equal to zero. A vertical line has no slope).

**Calculating the slope.**

How to calculate the slope of a line can be found on many math sites and youtube. The explanation I would give does not differ much from everything that is on the internet. The only thing that could possibly be an addition is the order in which I would give the explanation.

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