BIM 3.2 Linear Functions

BIM 3.2 Linear Functions

What is a linear function?

Which of these is a linear function?

It is a graph where the line does not change direction and has the same rate of change!

Let us try some tables.

Which of these three tables is a linear function?

Table 1 the x changes how much each time?

How much does the y change?

They must be the same if it is a linear function. x: +2 y: +8, +16,+24,....Not linear.

Table 2: How much does it change?

Is it linear?

Table 2: How much does it change?

Is it linear?

X is linear at +1 rate.

Y is not linear.

Table 2:

X is linear at +1 rate.

Y is not linear. It goes up and down at different rates.

Is Table 3 Linear?

Work it out at your table.

Table 3:

X goes up 2 every time.

The y goes down 4 every time.

It is linear!

Table 3:

The slope is y/x or rise over run.

Slope is y/x=-4/2=-2

We will need that later.

Linear equations will have only a power of 1 on the variable. They will be in the form y=mx+c.

Examples of linear equations!

y=x

y=x+1

y+5x=9

-3x+y=-6

Which of these equations is linear?

 $y=x^2+1$  
 $y=2x+3$  
 $y=x^{-1}+2x+5$  

So we can now recognize linear equations by graph, table, and equation.

Discreet linear graph.

Domain: (1,2,3,4,5,6)

Range: (150,300,450,600,750,

900)

Example: Monthly counts of visitors.

Continuous Linear 

Graph!
Domain:  $-\infty<x<\infty$  

Range:  $-\infty<x<\infty$  

Examples:  Equation for continuous count of visitors at any time.

Homework is on page 117: 6-48 every third problem. Quizizz practice on joinmyquiz.com

Code on board!

Joke of the Day: What did the mermaid wear.

Wait for it.....An Algae-Bra.

Get it, yeah...?