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Unit 3 – Writing & Graphing Linear EquationsSection 1 – Graphing Relationships

We use _____________ to show a relationship between ___________________.

The air temperature was constant for several hours at the beginning of the day and rose steadily for several hours. It stayed the same temperature for most of the day before dropping sharply at sundown. Choose the best graph below to represent this situation:

Step 1: Read the graph from left to right to show time passing.

Step 2: List key words in order.

Step 3: Pick the graph that shows the math words in order.

Key Words Math Words

The correct graph is __________.

1

Each day several leaves fall from a tree. One day a gust of wind blows off many leaves. Eventually, there are no more leaves on the tree. Choose the graph that best represents the situation.

The correct graph is _________________.

Sketch a graph for the following situation.

A truck driver enters a street, drives at a constant speed, stops at a light, and then continues.

Sketch a graph for the following situation.

The level of water in a bucket stays constant. A steady rain raises the level. The rain slows down. Someone dumps the bucket.

Sometimes a graph can look like this:

2

A pet store is selling puppies for $50 each. It has 8 puppies to sell.

Some graphs are connected lines or curves called _______________. Some graphs are only distinct points. They are called _____________.

Sketch a graph for the situation. Tell whether the graph is continuous or discrete.

A small bookstore sold between 5 and 8 books each day for 7 days.

3

Unit 3 – Writing & Graphing Linear EquationsSection 2 – Scatter Plots & Lines of Best Fit

A scatter plot is:

4

A correlation

A correlation

What do you notice about how the data looks?

A _______________________, or _____________________ is drawn on scatter plots to make predictions.

A scatter plot looks like this:

5

Based on the trend line, predict how many wrapping paper rolls need to be sold to raise $500.

Draw a line that has about the same number of points above and below it. Your line may or may not go through data points.

Find the point on the line whose y-value is __________.

The corresponding x-value is about ___________.

The scatter plot shows the number of orders placed for flowers before Valentine’s Day at one shop. Based on this relationship, predict the number of flower orders placed on February 10.

The scatter plot shows a relationship between the total amount of money collected at the concession stand and the total number of tickets sold at a movie theater. Based on this relationship, predict how much money will be collected at the concession stand when 150 tickets have been sold.

Unit 3 – Writing & Graphing Linear EquationsSection 3 – Writing Functions

Write the nth term. Write the equation.

Now Next

0 5

6

x y

0 5

1 6

2 7

3 8

n ?

Example #1

1 6

2 7

3 8

n ?

7

Example #2

Example #3

Example #4

Example #5

Unit 3 – Graphing Linear EquationsSection 4 – Day 1 - GRAPHING FUNCTIONS

8

Example #6 Example #7

Example #8Example #9

Example #10

(9, -142)

y = 4xAn ordered pair… A table of values… A graph…

y = 2x - 49

EX #1

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

10

EX #2

YOU TRY

y = 4x + 1

A mouse can run 3.5 meters per second. The function y = 3.5x describes the distance y the mouse can run in x

seconds. Graph the function.

Use the graph to estimate how manymeters a mouse can run in 2.5 seconds.

The fastest recordedHawaiian lava flow moved

at an average speed of 6 miles per hour.The function y = 6x describes the distance y the lava moved on average in x hours.

Use the graph to estimate how many milesThe lava moved after 5.5 hours.

11

EX #3

YOU TRY

Unit 3 – Graphing Linear EquationsSection 4 – Day 2 - GRAPHING FUNCTIONS

2x + y = 8

Step 1: Solve for y.

Step 2: Set up a table of valuesand choose your x-coordinates.

Step 3: Plug the x-coordinates into the equation to find they-coordinates.

Step 4: Plot your points.(should see pattern)

Step 5: Connect your points.(it should be a LINE)

13

EX #1

EX #2

EX #3

Unit 3 – Writing & Graphing Linear EquationsSection 5 – Identifying Functions

14

EX #4

Identifying Linear Functions from a Graph:

Identifying Linear Functions from an Equation:

Linear Graphs: Linear Equations:

15

Identifying Linear Functions from a Table of Values:

x y-2 6-1 30 21 32 6

16

1. (3, 0), (-1, 2), (1, 6), (3, 12), (5, 20)

2. (3, 4), 5, 7), (7, 10), (9, 13), (11, 16)

3.

4. 3y = 12

17

YOU TRY

Unit 3 – Writing & Graphing Linear EquationsSection 6 – Intercepts – Day 1 Notes

18

Vocabulary

The y-intercept is

The x-intercept is

Finding Intercepts from a Graph

The graph intersects the The graph intersects the

______________ at _______. ________________ at _______.

The ________________ is ____. The ________________ is ____.The graph intersects the The graph intersects the

________________ at _______. ________________ at _______.The ________________ is ____. The ________________ is ____.

The graph intersects the x-axis at: The graph intersects the x-axis at:

The x-intercept is: The x-intercept is:

The graph intersects the y-axis at: The graph intersects the y-axis at:

The y-intercept is: The y-intercept is:

Finding Intercepts from a Table of Values

What do all y-intercepts have in common?

19

Ex #1 Ex #2

YOU TRY

What do all x-intercepts have in common?

x y0 -85 -410 0

The graph intersects the The graph intersects the

______________ at _______. ________________ at _______.

The ________________ is ____. The ________________ is ____.The graph intersects the The graph intersects the

________________ at _______. ________________ at _______.The ________________ is ____. The ________________ is ____.

x y-7 -10 07 1

20

The graph intersects the x-axis at:

The x-intercept is:

The graph intersects the y-axis at:

The y-intercept is:

The graph intersects the x-axis at:

The x-intercept is:

The graph intersects the y-axis at:

The y-intercept is:

x y-6 00 26 4

x y0 -82 -44 0

21

YOU TRY

Unit 3 – Writing & Graphing Linear EquationsSection 6 – Intercepts – Day 2 Notes

22

x-intercepts y-intercepts

The ____________ on a line that crosses the _______________.

The ____________ on a line that crosses the _______________.

The _______________________ is ALWAYS ________.

The _______________________ is ALWAYS ________.

Ex: Ex:

Finding Intercepts from an Equation

y = -2.5x + 5.75

Estimate the y-intercept to the nearest tenth.

Estimate the x-intercept to the nearest tenth.

x-intercepts y-interceptsThe _______________________ is

ALWAYS ________.

The _______________________ is ALWAYS ________.

23

Ex #1

●

●

y = 0.45x – 3.7

Estimate the y-intercept to the nearest tenth.

Estimate the x-intercept to the nearest tenth.


ALWAYS ________.The _______________________ is

ALWAYS ________.

24

Ex #2

●

●

Calculate the x and y intercepts.

5x – 2y = 10


ALWAYS ________.The _______________________ is

ALWAYS ________.

25

Ex #3

Find the x & y intercepts. Write your answers as ordered pairs. Graph your line by graphing the intercepts.

-3x + 5y = 30

13x – 2y = 33.8

26

YOU TRY

Unit 3 – Writing & Graphing Linear EquationsSection 7 – Slope – Day 1 Notes

Line #1: x-intercept = y-intercept =

Line #2: x-intercept = y-intercept =

Slope is:____________________________________

A rate of change is a _____________________.

The slope of a line refers to…27

The slope of a line is ______________________________________

____________________________________________________

Find the slope of the line.

Find the slope of the line that contains (0, -3) and (5, -5).

28

On a coordinate plane, the slope of a line also refers to the…

Tell whether the slope of each line is positive, negative, zero, or undefined. Then find the slope.

29

1) Find the slope of the line passing through the points (-1, 3) and (4, -6)

2) Find the slope of the line passing through the points (-5, 3) and (9, 3)

Unit 3 – Writing & Graphing Linear EquationsSection 7 – Slope – Day 2 Notes

Finding slope from a GRAPH

30

YOU TRY

Finding slope from a TABLE-Determine the x and y intercepts if possible

x y

0 22 14 06 -1

x y

0 71 42 13 -2

31

YOU TRY

Ex #1 Ex #2

Determine the x and y intercepts

Determine the x and y intercepts

Slope: Slope:

What will this graph What will this graphlook like? look like?

1) 2)

Slope:Slope:

What will this graph What will this graph

look like?look like?

x y

-3 990 983 976 96

x y

2 84 126 168 20

32

YOU TRY

(-1.3, 1.62)(5.76, 4.1)

Find the slope of the line that contains the points (28, 52) and (8, 1).

What will this graph look like?

Find the slope of the line that contains the points (-8, 232) and (-8, 95).

What will this graph look like?

1) Find the slope of the line that contains (-20, 2) and (71, -2).

2) Find the slope of the line that contains (53, -7) and (6, -47).

3) Which line is steeper?

33

Ex #2

Ex #1

YOU TRY

Unit 3 – Writing & Graphing Linear EquationsSection 8 – Slope-Intercept Form – Day 1 Notes

Slope-Intercept Form

34

Writing Equations in Slope-Intercept Form

From a sentence

Write the equation of a line with a slope of 6 and a y-intercept of 84.

Write the equation of a line with a slope of 17 and a y-intercept of -33.

Graphing Equations in Slope-Intercept Form

Graph the function y = 4x – 3.

Is the equation in slope-intercept form?

Identify the slope x-intercept and y-intercept.

Graph the function

Is the equation in slope-intercept form?

Identify the slope and y-intercept.

35

EX #1

EX #2

EX #1

EX #2

Graph the following functions.

1. y = -5x + 8 2.Identify the x and y intercepts Identify the x and y interceptsCalculate if necessary. Calculate if necessary.

36

YOU TRY

Graphing Equations given two points

(3, 5) and (0, -4)

m =

b =

Graphing Equations given a table

x 3 4 5 6y -6 -4 -2 0

m =

b

37

Unit 3 – Writing & Graphing Linear EquationsSection 8 – Slope-Intercept Form – Day 2 Notes

Graph the function 38

Ex #1

Identify or calculate the x and y intercepts

Graph the function 2x – 4y = 10 Identify or calculate the x and y intercepts

Graph the function x + 3y = 9 Identify or calculate the x and y intercepts

Graph the function 3x + 2y = -4Identify or calculate the x and y intercepts

39

Ex #2

You Try #1

You Try #2

.

SPECIAL TYPES OF LINES.

Graph the following functions. Determine the x and y intercepts

x = -4 y = 10

From a graph.

Write an equation for the line. Identify or calculate the x and y intercepts

40

Ex #1 Ex #2

41

You Try #1

You Try #2

Unit 3 – Writing & Graphing Linear EquationsSection 9 – Parallel & Perpendicular Lines – Notes

42

1) Parallel, Perpendicular, or Neither? 1) Parallel, Perpendicular, or Neither?

43

#1 #2

2) Why? 2) Why?

3) m = m = 3) m = m =b = b = b = b =

___________________ ___________________

___________________ ___________________


44

#3 #4

2) Why? 2) Why?

3) m = m = 3) m = m =b = b = b = b =

___________________ ___________________

___________________ ___________________


45

You Try #1 You Try #2

2) Why? 2) Why?

3) m = m = 3) m = m =b = b = b = b =

___________________ ___________________

___________________ ___________________

Unit 3 – Writing & Graphing Linear EquationsSection 10 – Finding “b” – Day 1 Notes

46

2) Put the slope in for m.

3) Choose one ordered pair and put the x-coordinate in for x and the y-coordinate in for y.

4) Solve for b.

5) Write your final answer.

48

Ex #1

Write the equation of the line.

1) Find the slope.



4) Solve for b.


49

Ex #2

Write the equation of the line.1) Find the slope.



4) Solve for b.


Unit 3 – Writing & Graphing Linear EquationsSection 10 – Finding “b” – Day 2 Notes

50

Ex #3

You Try

Write the equation for the table.

51

Ex #1

1) Find the slope.

x y

14 248

15 262

16 276



4) Solve for b.


52


1) Find the slope.

x y

-7 154

-5 112

3 -56



4) Solve for b.


53

Ex #2

Write the equation for the table.x y

-10 97

-8 75

-6 53


x y

13 -50

15 -34

17 -18

Unit 3 – Writing & Graphing Linear EquationsSection 11 – Translating – Notes

54

Ex #3

You Try

Graph

Use a different colored pencil and graph on the same coordinate plane.

Describe the differences between the graphs.

Describe the differences between the equations.

What stayed the same? What’s different?

Graph

Use a different colored pencil and graph on the same coordinate plane.

Describe the differences between the graphs.

Describe the differences between the equations.

What stayed the same? What’s changed?

55

Ex #1

Ex #2

#1 Graph

#2 Graph

Describe the translation from #1 to #2.

Translate the graph 8 units down.

Write the new equation.

If the slope of y = 3x + 5 is changed to its negative reciprocal but everything else stays the same, what is the new equation?

56

Ex #3

Ex #4

Ex #5

Compare the slope and y-intercept in the two equations.

Graph the equation

Graph the equation

ALL VERTICAL LINES….ALL HORIZONTAL LINES…..

x y

x y

57

Ex #6

Ex #7

Ex #8

Unit 3 – Writing & Graphing Linear EquationsSection 12 –Word Problems – Notes

An oil tank is being filled at a constant rate. The table shows the depth of oil is a function of the number of minutes the tank has been filling. Write an equation that represents the table.

58

Ex #1

1. Do I know my y-intercept?

2. Find the depth of oil after one half-hour

Helen is in a bicycle race. She has already biked 10 miles and is now biking at a rate of miles per hour. Her distance as a function of time is shown in the graph.

1. Write an equation to show the relationship betweenthe distance biked and the time in hours.(HINT use y=mx+b)

2. Identify the slope and y-intercept and describe their meanings.

3. How far will Helen have biked after 3 hours?

Toni is finishing a scarf at a constant rate. The table shows the number of hours Toni has spent knitting this week and the corresponding rows in the scarf.

1. Write an equation is slope intercept form to best represent this linear function.

59

Ex #2

You Try #1

2. How many rows has Toni knitted after 10 hours?

A closet organizer charges $100 initial consultation fee plus $30 per hour. The cost as a function of the number of hours worked is graphed.

1. Write an equation that represents the cost as a function of the number of hours worked.

2. Identify the slope and the y-intercept and describe their meanings.

3. How much money will the organizer make after 10 hours?

60

You Try #2

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