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
