# Pending - Examples, Exercises and Solutions

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

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

This calculation is done using the following formula:

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

where the two points $\left(X1,Y1\right)$ and $\left(X2,Y2\right)$ 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.

## Practice Pending

### Exercise #1

Choose the correct answer for the function.

$y=-x+1$

### Step-by-Step Solution

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.

The graph is parallel to the graph of function

$y=-1-x$

### Exercise #2

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

Negative slope

### Exercise #3

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

Negative slope

### Exercise #4

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

Negative slope

### Exercise #5

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

Negative slope

### Exercise #1

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

Negative slope

### Exercise #2

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

Negative slope

### Exercise #3

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

Positive slope

### Exercise #4

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

Positive slope

### Exercise #5

Given the linear function:

$y=1-4x$

What is the rate of change of the function?

### Video Solution

$m=-4$

### Exercise #1

Given the linear function:

$y=10-2x$

What is the rate of change of the function?

### Video Solution

$m=-2$

### Exercise #2

Given the linear function:

$y=-6x$

What is the rate of change of the function?

### Video Solution

$m=-6$

### Exercise #3

Given the linear function:

$y=x-4$

What is the rate of change of the function?

### Video Solution

$m=1$

### Exercise #4

Given the linear function:

$y=16+16x$

What is the rate of change of the function?

### Video Solution

$m=16$

### Exercise #5

Given the linear function:

$y=7-3x$

What is the rate of change of the function?

### Video Solution

$m=-3$