Unit 6

Graphing Linear

Equations

NAME:______________________ GRADE:_____________________ TEACHER: Ms. Schmidt _

Lesson 1 Homework

Solving a Linear Equation for y Solve each equation for y and state the slope and y-intercept.

1. 2x + y = 5 2. –x + 2y = 12 3. 3x – 4y = 8 4. x – y = 7

5. 3x = y + 1 6. y – 4x = 4 7. 5x + 5y = 15 8. 9y – 2x = 27

9) Evaluate each expression for n = 3

a. 2n + 5 – n b. 3n+18

3n

c. 24

· n 4–n

10) Simplify:

a) 54∙58 b) 4x2(3x) c) (5x)0 d) 5x0 e) 6-4∙6-3

A. Steps for Graphing a linear equations using a table:

Lesson 2 Classwork

Graphing a Line from a Table

1.

2.

3.

4.

1. y = 2x - 5 2. y = 1

x + 2 3

3. 2x + y = 1 4. 4y + 2x = 16

x y (x,y)

x y (x,y)

x y (x,y)

x y (x,y)

x y (x,y)

3. 6 + y = 2x 4. 2x – y = 4

x y (x,y)

x y (x,y)

x y (x,y)

Try These: 1. y = 3x - 4

2. y = -x

Graph each line using a table of values.

1. y = 3x - 6 2. y =

1 x +1

2

Lesson 2 Homework

Graphing a Line from a Table

3. -3x + y = -4 4. 3y + 6x = 9

Review:

5) Simplify: (3x – 5) – (x + 3) + (-2x + 7) 6) Simplify: 64 - 42

÷ 8

x y (x,y)

x y (x,y)

x y (x,y)

x y (x,y)

Lesson 3 Classwork

Graphing a Linear Equations using Slope and Y-Intercept

Graphing Linear Equations without a table

Graph the line: y = 2x - 5

Steps

1)

2)

3)

4)

5)

Lesson 3 Classwork

Graphing a Linear Equations using Slope and Y-Intercept

1) y

x

2) y x

3) y x

4) y

x

5) y x 6) y

y

x

y

x

y

x

y

x

y

x

y

x

Graph the following lines.

Lesson 3 Homework

Graphing a Line using Slope and y-intercept

1) y = -2x + 1 2) y = 3x

3) slope = 0 y-intercept = -3 4) x = 2 5) y = -5

6) Given y = 5 - 3x , what is the slope of the line?

7) Given y = -7 - 4x, what is the y -intercept of the line?

8) If the slope of a line is ½ and the y-intercepts is 3, what is the equation of the line?

Lesson 4 Classwork

Graphing a Line using Slope and y-intercept

Sketch the graph of each line.

1) x y

2) x y

3) x y 4) x

5) x y 6) x y

y

x

y

x

y

x

y

x

y

x

y

x

7) x y 8) x y

9) y 10) x y

11) x y 12) x y

y

x

y

x

y

x

y

x

y

x

y

x

1) y = -5x 2) y = -5

4s

Lesson 4 Homework

Graphing a Line using Slope and y-intercept

Graph the following using slope/y-intercept: Name the type of slope for each line.

2

3) y = - 3

x + 7 4) 2x + y = 4

5) Simplify each expression:

5 5 3

3 2 –8 46∙65∙43

a) 2s2 b) (2x ) c) 7 ∙ 5 ∙ 7 d)

4∙62

6) Rewrite 81 in exponential form using 3 as the base. 7) Solve: 8 + 1

x = −1 + 3

x 2 4

Lesson 5 Classwork

Writing a Function Rule

Vocabulary:

Input values:

Output values:

Relation:

Function:

Function Rule:

Making Function Tables

To find the output values of a function, substitute the input values for the variable in the function rule.

1) y = 2x + 1

2) y = x + 2 3) y = x – 4

4) What is the output for an input of 7 if the function rule is 4n?

5) If the output is 4 and the function rule is n + 3, what is the input?

Input (x)

Output (y)

-1

0

2

Input (x)

Output (y)

2

4

8

Input Function Rule Output Ordered pairs

x 2x + 1 Y (x,y)

0

1

2

Finding Function Rules

This year, the only function rules you will write will be linear equations. To write a function rule, then, is to

write a liner equation!

What is the slope?

What is the y-intercept?

Write the equation for the line (function rule)

Write an equation for each given function (Function rule).

1) 2)

x y

-2 -7

-1 -4

0 -1

3) 4)

x 6 4 2

y 3 2 1

Hours 20 25 35

Pay ($) 160 200 240

Input (x)

Output (y)

1 2

2 5

3 8

n t

1 4

2 8

3 12

Lesson 5 Homework

Understanding Functions

Write the function rule for the following table, fill in the missing y-value in the table, and graph the function.

Input Output

-2 -4

-1 -2

0 0

1

Function Rule:

Write an equation for the function and find the missing value in the table:

2) 3)

m c

1 0

2 1

3 2

4 3

5 4

100

4) What is the output for the function rule y = -3x – 2 if the input is 10?

5) What is the input for the function y = 2x – 5 if the output is -11?

x y

0 0

1 20

2 40

3 60

4 80

27

x

5

6

7

8

y

4

3

2

x

3

8

5

8

y

4

3

2

0

x

2 3

y

3

4

5

6

Vocabulary:

Lesson 6 Classwork

Function vs. Not a Function

Relation:

Domain:

Range:

Function:

Vertical Line Test:

Given the relation: {(1,2), (2, 4), (3, 5), (2,6), (1,-3)}

What is the domain?

What is the range?

Complete the following table and graph the function:

x y

Which relation represents a function?

1) 2) 3) 4)

Which relation diagram represents a function?

5) 6) 7) 8) Domain

Sue

Joe

Emma

Lilly

Range

Blue

Red

Pink

x y

0 -4

1 -1

2 2

3 5

4 8

x y

0 1

2 1

4 1

6 1

8 1

x y

0 5

1 6

2 7

1 8

0 9

x y

12 -2

10 -1

8 0

10 1

6 2

12)

Domain

A B C D

Range

1 2

Domain

Beth Sally Lucy Jen

Range

Dave Mike Ryan Dan

Using the vertical line test state whether or not each relation is a function.

9) 10) 11)

Try These: Which of the following represents a function?

1) 2) 3) 4)

5) 6) 7) 8)

9) 10) 11) 12)

13) 14)

Which set of ordered pairs represents a

function?

1)

2)

3)

Which set of ordered pairs is not a function?

1)

2)

3)

x y

1 7

5 5

9 3

1 1

Domain

2 3 4 5

Range

1 2 3

13)

x y

5 2

7 3

9 4

11 5

5 6

x y

-2 2

-1 5

0 4

1 5

1) Which of the relations below is a function?

A) {(2,3), (3,4), (5,1), (6,2), (2,4)}

B) {(2,3), (3,4), (5,1), (6,2), (7,3)}

C) {(2,3), (3,4), (5,1), (6,2), (3,3)}

Lesson 6 Homework

Function vs. Not a Function

2) Given the relation A = {(5,2), (7,4), (9,10), (x, 5)}. Which of the following values for x will make relation A a function?

A) 7 B) 9 C) 4

3) The following relation is a function.

{(10,12), (5,3), (15, 10), (5,6), (1,0)}

A) True B) False

4) Which of the relations below is a function?

A) {(1,1), (2,1), (3,1), (4,1), (5,1)}

B) {(2,1), (2,2), (2,3), (2,4), (2,5)}

C) {(0,2), (0,3), (0,4), (0,5), (0,6)}

5) The graph of a relation is shown at the right. Is this relation a function?

A) Yes

B) No

C) Cannot be determined from a graph

6) Is the relation depicted in the chart below a function?

A) Yes

B) No

C) Cannot be determined from a chart

7) The graph of a relation is shown at the right. Is the relation is a function?

A) Yes

B) No

C) Cannot be determined from a graph

Are the following graphs Linear or Non-linear? (Which ones are Linear Functions?)

7)

Lesson 7 Classwork

Linear vs. Non-Linear

Are the following equations Linear or Non-linear? (Which ones are Linear Functions?)

9) y x 3 3x 9 10) y x 2 11) y

2 10

x 12) y x

2 x 2

13) y = 5x 14) y = 2 15) 16) x = 8 16) y = |x + 7|

Are the following tables Linear or Non-linear? (Which ones are Linear Functions?)

17) 18) 19) 20)

Are the following word problems Linear or Non-linear?

21) Sam put $10 in the box under his bed every week

22) A dolphin jumps above the surface of the ocean water, then dives back in the water.

23) A soccer player sprints from one side of the field to the other.

24) A lacrosse player throws a ball upward from her playing stick with an initial height of 7ft and an initial velocity of 90 ft. per second.

25) A rocket is shot off into the air and then comes back down to the ground.

26) Bill borrows $2,500 from the bank and has to pay it off monthly for 30 months.

3) 4)

5) 6)

* 8)

3

Are the following Linear or Non-linear?

Lesson 7 Homework

Linear vs. Non-Linear

1) y = x2 − x − 2 2) y = |x + 1| 3) y = 5x + 2 4) y = x3 − 3x + 9 5) y − 7x = −2

6) 7) 8) 9)

10) A baseball player hits a pop fly

11) The path traveled by a basketball during a shot on the basket

12) A babysitter getting paid $6 per hour

13) You deposit $250 per year for 39 years

14) 15) 16) 17)

18) Which equation represents a linear function?

A. y = 8x4

B. y = 0.05x – 0.01

C. y = 2x2

+ 5

D. √x

19) Which of the following does not describe a linear function?

A. the perimeter, p, of a square with side s: p = 4s

B. the circumference, C, of a circle with radius r: C = 2nr C. the salary, s, of an employee making $12.50 per hour, h: s = 12.50h

D. the area, A, of a circle with radius r: A = nr2