Slope in the Function y=mx

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The concept of slope in the function y=mx y=mx expresses the angle between the line and the positive direction of the X X axis.
M M represents the slope of the function – the rate of change of Y Y relative to the rate of change of X X .
When two points on a certain line are known, the slope of the line can be calculated from them. 

If M>0 M>0 is positive - the line rises
If M<0 M<0 is negative - the line falls
If M=0 M=0 the line is parallel to the X X axis. (In a graph like this, where b=0 b=0 the line coincides with the X X axis.)

This calculation is done using the following formula: 

 m=(Y2Y1)(X2X1)  m=\frac {(Y2-Y1)}{(X2-X1)}

where the two points (X1,Y1) \left(X1,Y1\right) and (X2,Y2) \left(X2,Y2\right) are on the mentioned line. 

It is important to emphasize that the slope is constant for any line. 


The greater the slope – the steeper the graph.
The smaller the slope – the more moderate – flatter the graph.
How will you remember this?
Remember that when the slope is equal to 0, the graph is parallel to the X-axis – it is very, very moderate – flat.
Therefore, as it increases, the graph will be steeper.

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For the function in front of you, the slope is?


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Examples of questions on the topic of the slope of a function

Which of the graphs has a greater slope?
We see that the orange graph is "flatter" than the purple graph, so the slope of the purple graph is greater.

Example 1:

Given two points (1,5) \left(1,5\right) and (2,8) \left(2,8\right) .

We know that the two points lie on a certain line.
We are asked to find the slope of the line.
We will use the formula mentioned earlier and substitute the values:

( m=\frac{(8-5)}{(2-1)}= \frac{3}{1}=3 )

In other words, the result we obtained is actually the slope of the desired line.

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Example 2:

Let's see an example of finding the slope:

Given two points that the line passes through: (2,4),(5,1) \left(2,4\right),\left(5,1\right)
We will calculate the slope using the formula:

m=(14)(52)=33=1 m=\frac{(1-4)}{(5-2)}= \frac{-3}{3}=-1

The slope of the line is −1.
We can sketch a graph, considering the two points it passes through and the fact that its slope is negative – a descending line.

(Image 1)

Do you know what the answer is?
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