**Linear and Nonlinear Functions**

Objective

SWBAT determine if a function is linear or non-linear.

SWBAT interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

Do Now

The table shows the approximate height and length traveled by a football thrown at an angle of 30 degrees with an initial velocity of 30 yards per second.

Linear Functions

Functions are considered linear when they have graphs that are straight lines and represent constant rates of change

Exit Ticket

Answer each question and explain your reasoning for each.

**Review**

Nonlinear Functions

Functions that do not have constant rates of change. Therefore, their graphs are not straight lines.

8.F.A.3

1. Did the football travel the same height each half-second? Justify your answer.

3. Graph the ordered pairs (time, height) and (time, length) on separate grids. Connect the points with a straight line or smooth curve. Compare the graphs.

2. Did the football travel the same length each half-second? Justify your answer.

Linear or Nonlinear?

Determine whether each table represents a linear or nonlinear function. Explain.

**Review**

Remember we learned that functions represent a relationship between inputs and outputs. They can also be expressed as formulas, ordered pairs, and graphs.

Linear or Nonlinear?

Determine whether each table represents

a linear or nonlinear function. Explain

Linear or Nonlinear?

Determine whether each graph represents a linear or nonlinear function. Explain.

Linear or Nonlinear?

Determine whether each table represents

a linear or nonlinear function. Explain

Linear or Nonlinear?

Determine whether each table represents

a linear or nonlinear function. Explain

Linear or Nonlinear?

Determine whether each equation represents a linear or nonlinear function. Explain.

Linear or Nonlinear

Determine whether each graph represents a linear or nonlinear function. Explain.

y = x + 4

y =

6

x

Since the equation can be written as

y = 1x + 4

, this function is linear

The equation cannot be written in the form

y = mx + b

. So, this function is nonlinear

Linear or Nonlinear?

Determine whether each equation represents a linear or nonlinear function. Explain.

1.

y = 2x + 1

2.

y = 3x

3.

y = x - 4

2

Remember we learned that functions represent a relationship between inputs and outputs. They can also be expressed as formulas, ordered pairs, and graphs.

Do Now

Molly earns $5 for each hour she babysits plus $12 to cover any personal expenses. Suzie earns $4 for each hour she babysits plus $19 to cover personal expenses. At a certain point, Molly and Suzie will work the same number of hours and earn the same amount of money. At this point, how much money will each girl earn?

1. DVDs can be made in a factory in New Mexico at the rate of 20 DVDs per $3, but the factory costs $80,000 to build. If they make 1 million DVDs, what is the unit cost per DVD?

DVDs can be made in a factory in Colorado at the rate of 10 DVDs per $1.50, but the factory costs $100,000 to build. If they make 1 million DVDs, what is the unit cost per DVD?

How much can a buyer save on a million DVDs by buying DVDs from New Mexico instead of DVDs from Colorado?

Find an equation for the cost of making x number of DVDs in the factory in New Mexico.

Find an equation for the cost of making x number of DVDs in the factory in Colorado.

Task

Objective

SWBAT graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

Survey

https://www.surveymonkey.com/r/G38ZCWJ

Do Now

Directions: Tell whether the following are functions or not, if it is linear or nonlinear. If it is linear, what is the rate of change?

1.

2.

You work for a video streaming company that has two monthly plans to choose from:

Plan 1: A flat rate of $7 per month plus $2.50 per video viewed

Plan 2: $4 per video viewed

What type of functions model this situation? Explain how you know.

Define variables that make sense in the context, and then write an equation with cost as a function of videos viewed, representing each monthly plan.

How much would 3 videos in a month cost for each plan? 5 videos?

Compare the two plans and explain what advice you would give to a customer trying to decide which plan is best for them, based on their viewing habits.

Video Streaming Task