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Patterns And Linear Functions

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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.

An example of this would be the function:
 y = 4x
 y = 4(1) = 4
 y = 4(2) = 8
 y = 4(3) = 12
This function increases at a constant rate, as the input increases or decreases at a constant rate.

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 x in a linear function, it will come out as y.

For example when we have x = 0 our y = 3. If x = 2, y = 9 and if x = 7, y = 28.

So how does this relates to linear functions?

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

Here’s an example of a linear function:

When x = 0, y = 3,
when x = 1, y = 5,
if x = 2, y = 7,
when x = 3, y = 9,
and when x = 4, y = 11.

What makes this linear just by looking at this?

It’s because it increases at a constant rate.

When x increase by 1, y increase by 2.

Another example:

When x = 3, y = 15,
when x = 4, y = 19,
if x = 5, y = 23,
when x = 6, y = 27,
and when x = 7, y = 31.

Here when x increase by 1, y increase by 4.

Now, let’s graph this.

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

Patterns and Linear Functions

Let’s have another example:

When x = 0, y = 0,
when x = 1, y = 3,
if x = 2, y = 6,
when x = 3, y = 9,
and when x = 4, y = 12

Here, its y = 3x.

Another example is:

When x = 0, y = 0,
if x = 1, y = 4,
when x = 2, y = 8,
and when x = 3, y = 12

Here, y = 4x.

So we have

y = 4x

y = 4(0) = 0
y = 4(1) = 4
y = 4(2) = 8
y = 4(3) = 12

Same thing with the example above.

But they don’t always work out this way.

Let’s have a more complicated example.

When x = 0, y = 2,
when x = 1, y = 5,
if x = 2, y = 8,
when x = 3, y = 11,
and when x = 4, y = 14

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

Here, we’re going to have a

y = 3x + 2

Let’s check using x = 4, let’s substitute

y = 3x + 2 y = 3(4) + 2 y = 12 + 2 y = 14