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