Linear Function y=mx+b: Determine the slope of a linear function

Given the linear function:

$y=x-4$

What is the rate of change of the function?

Let's remember that the rate of change equals the slope.

In this case, the slope is:

$m=1$

$m=1$

Which best describes the function below?

$y=2-3x$

Remember that the rate of change equals the slope.

In this function:

$m=-3$

Therefore, the function is decreasing.

The function is decreasing.

Choose the correct answer for the function.

$y=-x+1$

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.

_{The graph is parallel to the graph of function}

_^$y=-1-x$

Given the linear function:

$y=1-4x$

What is the rate of change of the function?

$m=-4$