1

Unit 3 – Writing & Graphing Linear Equations Section 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 __________.

2

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.

3

Sometimes a graph can look like this: 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.

4

5

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

A correlation A correlation

What do you notice about how the data looks?

A scatter plot is:

A scatter plot looks like this:

6

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

7

Unit 3 – Writing & Graphing Linear Equations Section 3 – Writing Functions

Write the nth term. Write the equation. Now Next

0 5

1 6

2 7

3 8

n ?

x y

0 5

1 6

2 7

3 8

n ?

Example #1

Example #2

Example #3

Example #4

8

Example #5

Example #6 Example #7

Example #8 Example #9

Example #10

9

Unit 3 – Graphing Linear Equations Section 4 – Day 1 - GRAPHING FUNCTIONS

(9, -142)

y = 4x An ordered pair… A table of values… A graph…

10

y = 2x - 4

Step 1: Step 2: Step 3: Step 4: Step 5: y x= −1 2

2

EX #2

EX #1

11

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 many meters a mouse can run in 2.5 seconds. The fastest recorded Hawaiian 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 miles The lava moved after 5.5 hours.

YOU TRY

EX #3

YOU TRY

12

13

Unit 3 – Graphing Linear Equations Section 4 – Day 2 - GRAPHING FUNCTIONS

2x + y = 8 Step 1: Solve for y. Step 2: Set up a table of values and choose your x-coordinates. Step 3: Plug the x-coordinates into the equation to find the y-coordinates. Step 4: Plot your points. (should see pattern) Step 5: Connect your points. (it should be a LINE)

6x − y = 7

EX #1

EX #2

14

x y− =2 4 8

x y+ = −3

EX #3

EX #4

15

Unit 3 – Writing & Graphing Linear Equations Section 5 – Identifying Functions

Identifying Linear Functions from a Graph: Identifying Linear Functions from an Equation:

16

Linear Graphs: Linear Equations: Identifying Linear Functions from a Table of Values:

x y

-2 7

-1 4

0 1

1 -2

2 -5

x y

-2 6

-1 3

0 2

1 3

2 6

17

1. (3, 0), (-1, 2), (1, 6), (3, 12), (5, 20) 2. (3, 4), 5, 7), (7, 10), (9, 13), (11, 16) 3. y = 3− 2x 4. 3y = 12

YOU TRY

18

19

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

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:

Ex #1 Ex #2

YOU TRY

20

Finding Intercepts from a Table of Values What do all y-intercepts have in common? What do all x-intercepts have in common?

x y

0 8

5 -4

10 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 -1

0 0

7 1

21

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 0

0 2

6 4

x y

0 -8

2 -4

4 0

YOU TRY

22

23

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

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-intercepts The _______________________

is ALWAYS ________. The _______________________

is ALWAYS ________.

Ex #1

●

●

24

y = 0.45x – 3.7 Estimate the y-intercept to the nearest tenth. Estimate the x-intercept to the nearest tenth.

x-intercepts y-intercepts The _______________________

is ALWAYS ________. The _______________________

is ALWAYS ________.

Ex #2

●

●

25

Calculate the x and y intercepts.

5x – 2y = 10

x-intercepts y-intercepts The _______________________

is ALWAYS ________. The _______________________

is ALWAYS ________.

Ex #3

26

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

YOU TRY

27

Unit 3 – Writing & Graphing Linear Equations Section 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 _____________________.

28

The slope of a line refers to… • The slope of a line is ______________________________________ ____________________________________________________

Find the slope of the line.

29

Find the slope of the line that contains (0, -3) and (5, -5). On a coordinate plane, the slope of a line also refers to the… •

30

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

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)

YOU TRY

31

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

Finding slope from a GRAPH •

•

•

•

•

YOU TRY

32

Finding slope from a TABLE Slope: Slope: What will this graph What will this graph look like? look like? 1) 2)

Slope: Slope: What will this graph What will this graph look like? look like?

x y

0 2

2 1

4 0

6 -1

x y

0 7

1 4

2 1

3 -2

x y

-3 99

0 98

3 97

6 96

x y

2 8

4 12

6 16

8 20

Ex #1 Ex #2

YOU TRY

33

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?

Ex #2

Ex #1

YOU TRY

(-1.3, 1.62)

(5.76, 4.1)

34

35

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

Slope-Intercept Form 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 and y-intercept.

EX #1

EX #2

EX #1

36

Graph the function Is the equation in slope-intercept form? Identify the slope and y-intercept. Graph the following functions. 1. y = -5x + 8 2.

3 42

y x= − + EX #2

2 53

y x= −

YOU TRY

37

Graphing Equations given two points (3, 5) and (0, -4) m = b =

Graphing Equations given a table

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

m = b

38

39

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

Graph the function Graph the function 2x – 4y = 10 Graph the function x + 3y = 9

Ex #1

Ex #2

You Try #1

y x= +5 3

40

Graph the function 3x + 2y = -4 . SPECIAL TYPES OF LINES. Graph the following functions. x = -4 y = 10

You Try #2

41

From a graph. Write an equation for the line.

Ex #1 Ex #2

You Try #1

You Try #2

42

43

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

44

1) Parallel, Perpendicular, or Neither? 1) Parallel, Perpendicular, or Neither? 2) Why? 2) Why? 3) m = m = 3) m = m = b = b = b = b = ___________________ ___________________ ___________________ ___________________

#1 #2

= +2 2y x = −2 4y x = −8y x = +1 78

y x

45

1) Parallel, Perpendicular, or Neither? 1) Parallel, Perpendicular, or Neither? 2) Why? 2) Why? 3) m = m = 3) m = m = b = b = b = b = ___________________ ___________________ ___________________ ___________________

#3 #4

= 6y = −2x + =12 3 12x y − =4 1x y

46

1) Parallel, Perpendicular, or Neither? 1) Parallel, Perpendicular, or Neither? 2) Why? 2) Why? 3) m = m = 3) m = m = b = b = b = b = ___________________ ___________________ ___________________ ___________________

You Try #1 You Try #2

= −8x =5 x + =3 4 8x y = − −3 34

y x

47

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

48

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.

Ex #1

49

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

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.

Ex #2

50

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

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.

Ex #3

You Try

51

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

52

Write the equation for the table.

1) Find the slope.

x y

14 248

15 262

16 276

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.

Ex #1

53

Write the equation for the table. 1) Find the slope.

x y

-7 154

-5 112

3 -56

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.

Ex #2

54

Write the equation for the table. x y

-10 97

-8 75

-6 53

Write the equation for the table.

x y

13 -50

15 -34

17 -18

Ex #3

You Try

55

Unit 3 – Writing & Graphing Linear Equations Section 11 – Translating – Notes

Graph y x= Use a different colored pencil and graph

5y x= − 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 2 1y x= − + Use a different colored pencil and graph

2 5y x= − + on the same coordinate plane. Describe the differences between the graphs. Describe the differences between the equations. What stayed the same? What’s changed?

Ex #1

Ex #2

56

#1 Graph 2y x= #2 Graph 2 6y x= − Describe the translation from #1 to #2.

1 42

y x= +

Translate the graph 8 units down. Write the new equation.

Ex #3

5y x= −y x=

2 5y x= − +2 1y x= − +

Ex #4

57

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

Ex #5

Ex #6

2 4 16x y− + = −3 6 36x y− =

Ex #7 4x =

Ex #8 8y = −