4-6 Graphing Linear Functions pg. 248

Essential Question

How do you determine if a function is a linear function?

Graphing Review Video Clip- Standard Deviants

In your notebook:Write down 3 facts from the video clip.

1.2.3.

Definitions• linear equation- an equation whose graph is a line. The solutions of a linear equation are the points that make up its graph.

• linear function-a function whose graph is a non-vertical line.

The graph at right shows how far an inner tube travels down a river if the current flows 2 miles per hour. The graph is linear because all the points fall on a line. It is part of the graph of a linear equation.

Only two points are needed to draw the graph of a linear function. However, graphing a third point serves as a check. You can use a function table to find each ordered pair.

A Function (F) states the relationship between two variables.

( , )( , )2 8

It assigns a rule, that gives a unique

value to y in relation to the value of x.

RuleY = 4x

Function

RO filter RO filter RO filter

Input Rule Output

x 4x y

2

3

4

5

8

12

16

20

Functiony = 4x

4(2)

4(3)

4(4)

4(5)

Rule: y = x

Input outputI’ll push the pedal once.

I’ll push the pedal.

Every time you push the pedal, I’ll square your effort in rotations

2

Function

RO filter RO filter RO filter

Input Rule Output

x x y

2 2

3 3

4 4

5 5

4

9

16

Function

2

25

y = x2

2

2

2

2

Rule: y = 3x

Input output

I’ll give 3 gumballs for every quarter

I’ll push the pedal once.

I’ll put quarters in.

Function

RO filter RO filter RO filter

Input Rule Output

x 3x y

2 3(2)

3 3(3)

4 3(4)

5 3(5)

6

9

12

15

Functiony = 3x

x

y

0–2–4 2 4

2

4

–2

–4

Graph the linear function y = 4x - 1.Example 1

Input Rule Output Ordered Pair

x 4x – 1 y (x, y)

0

1

–1

4(0) – 1

4(1) – 1

4(–1) – 1

–1

3

–5

(0, –1)

(1, 3)

(–1, –5)

(0, –1)

(1, 3)

(–1, –5)

Graph the linear function y = 3x + 1.Input Rule Output Ordered Pair

x 3x + 1 y (x, y)

0

1

–1

3(0) + 1

3(1) + 1

3(–1) + 1

1

4–2

(0, 1)

(1, 4)

(–1, –2)

Example 2

x

y

0–2–4 2 4

2

4

–2

–4

(0, 1)

(1, 4)

(–1, –2)

The fastest-moving tectonic plates on Earth move apart at a rate of 15 centimeters per year. Scientists began studying two parts of these plates when they were 30 centimeters apart. Write a linear function that describes the movement of the plates over time. Then make a graph to show the movement over 4 years.

Example 3

Input Rule Output15(x) + 30x

0

2

4

15(0) + 30

15(2) + 30

15(4) + 30

y

30

60

90

x

y100

80

60

40

20

0 2 4 8 10 12

Cent

imet

ers

Years

Graphing Linear Equations Brain-Pop

Write down 2 facts about graphing linear equations.1.2.

Work Session

Linear Contemplations Worksheet Follow along as we review the directions

Homework

Workbook pg. 41All problems

Closing

The temperature of a liquid is decreasing at a rate of 12°F per hour. Susan begins measuring the liquid at 200°F. Write a linear function that describes the change in temperature over time. Then make a graph to show the temperature over 5 hours.

y = 200 – 12x