Pending - Examples, Exercises and Solutions

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. 

Note:

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.

Suggested Topics to Practice in Advance

  1. Function
  2. Linear Function
  3. The Linear Function y=mx+b
  4. Positive and Negativity of a Linear Function

Practice Pending

Exercise #1

Choose the correct answer for the function.

y=x+1 y=-x+1

Video Solution

Step-by-Step Solution

Let's start with option A

In a linear function, to check if the functions are parallel, you must verify if their slope is the same.

y = ax+b

The slope is a

In the original formula:

 y = -x+1

The slope is 1

In option A there is no a at all, which means it equals 1, which means the slope is not the same and the option is incorrect.

 

Option B:

To check if the function passes through the points, we will try to place them in the function:

-1 = -(-2)+1

-1 = 2+1

-1 = 3

The points do not match, and therefore the function does not pass through this point.

 

Option C:

We rearrange the function, in a way that is more convenient:

y = -1-x

y = -x-1

You can see that the slope in the function is the same as we found for the original function (-1), so this is the solution!

 

Option D:

When the slope is negative, the function is decreasing, as the slope is -1, the function is negative and this answer is incorrect.

Answer

The graph is parallel to the graph of function

y=1x y=-1-x

Exercise #2

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

XY

Video Solution

Answer

Negative slope

Exercise #3

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

XY

Video Solution

Answer

Negative slope

Exercise #4

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

XY

Video Solution

Answer

Negative slope

Exercise #5

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

XY

Video Solution

Answer

Negative slope

Exercise #1

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

XY

Video Solution

Answer

Negative slope

Exercise #2

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

XY

Video Solution

Answer

Negative slope

Exercise #3

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

XY

Video Solution

Answer

Positive slope

Exercise #4

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

XY

Video Solution

Answer

Positive slope

Exercise #5

Given the linear function:

y=14x y=1-4x

What is the rate of change of the function?

Video Solution

Answer

m=4 m=-4

Exercise #1

Given the linear function:

y=102x y=10-2x

What is the rate of change of the function?

Video Solution

Answer

m=2 m=-2

Exercise #2

Given the linear function:

y=6x y=-6x

What is the rate of change of the function?

Video Solution

Answer

m=6 m=-6

Exercise #3

Given the linear function:

y=x4 y=x-4

What is the rate of change of the function?

Video Solution

Answer

m=1 m=1

Exercise #4

Given the linear function:

y=16+16x y=16+16x

What is the rate of change of the function?

Video Solution

Answer

m=16 m=16

Exercise #5

Given the linear function:

y=73x y=7-3x

What is the rate of change of the function?

Video Solution

Answer

m=3 m=-3

Topics learned in later sections

  1. Finding a Linear Equation
  2. Graphical Representation of a Function that Represents Direct Proportionality
  3. Representation of Phenomena Using Linear Functions