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Postad: 29 apr 17:57

riktningskoefficient

can you explain that concept in english with some examples in english

naytte 4017 – Moderator
Postad: 29 apr 18:10 Redigerad: 29 apr 19:42

The slope kk of a line y=kx+my=kx+m is a number which tells you how much the function yy changes for a given change in xx. Graphically, it represents the steepness of the line. The greater the number kk, the steeper the line will be. Conversely, a smaller value of kk will result in a flatter line.

In English, there is the expression "rise over run". It is a mnemonic to help you remember the formula for the slope, namely:

k=ΔyΔx\displaystyle k=\frac{\Delta y}{\Delta x}

You "run" Δx\Delta x units in the xx-direction, and then correspondingly (according to the functional relationship) "rise" Δy\Delta y units in the yy-direction. 


Example:

A line y=kx+m\displaystyle y=kx+m goes through the points (0,1)(0,1) and (1,2)(1,2). Determine the function yy.

Since only a single line can go through two specific points at the same time, two points on the graph are enough to uniquely determine the line. We start by plugging in the first coordinate into our functional relationship:

y(0)=k·0+m=1m=1y(0)=k\cdot 0 +m=1 \implies m=1

Now we know the line can be written as y=kx+1y=kx+1. To determine the slope kk, we plug in the other point on the graph:

y(1)=k·1+1=2k=1y(1)=k\cdot 1 + 1 = 2 \implies k=1

Putting together what we know, we can determine the line to be:

y=x+1\displaystyle \implies y=x+1

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