This video shows how patterns in function charts give you different values. Linear functions are where the function output changes at a constant rate, relative to the input. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.

An example of this would be the function:

This function increases at a constant rate, as the input increases or decreases at a constant rate.

## Example of Patterns And Linear Functions

### Example 1

The linear function would be:

### Example 2

The linear function would be:

## Video-Lesson Transcript

Let’s go over patterns and linear functions.

Think of a linear function as a shape. When you put something in, it comes out as something else.

For example, when you put in a linear function, it will come out as .

For example when we have our . If , and if , .

So how does this relates to linear functions?

When we graph using and axis and we plot the -coordinates and -coordinates, we will form a straight line. That’s something special about the linear function.

Here’s an example of a linear function:

When , ,

when , ,

if , ,

when , ,

and when , .

What makes this linear just by looking at this?

It’s because it increases at a constant rate.

When increase by , increase by .

Another example:

When , ,

when , ,

if , ,

when , ,

and when , .

Here when increase by , increase by .

Now, let’s graph this.

You will see that it’ll give us a straight slash line.

Let’s have another example:

When , ,

when , ,

if , ,

when , ,

and when ,

Here, its .

Another example is:

When , ,

if , ,

when , ,

and when ,

Here, .

So we have

Same thing with the example above.

But they don’t always work out this way.

Let’s have a more complicated example.

When , ,

when , ,

if , ,

when , ,

and when ,

It’s not like our previous examples where it’s a simple equation.

Here, we’re going to have a

Let’s check using , let’s substitute