Extra Practice

Chapter 6

Topics Include:

Equation of a Line

y = mx + b & Ax + By + C = 0

Graphing from Equations

Parallel & Perpendicular

Find an Equation given…

Solving Systems of Equations

6.1 - Practice: The Equation of a Line in Slope y-Intercept Form: y = mx + b

1. Copy and complete the table.

Equation Slope

y-Intercept

a) y = 4x + 1

b) y =

2

x – 3

c) y = –2x

d) y = –x + 2

2. Find the slope and y-intercept of each line.

a)

b)

c)

d)

3. Write the equation of each line in question 2.

4. Write the equation of each line.

a)

b)

5. Write the equation of a line with each slope and y-intercept.

Slope y-Intercept

a) –2 1

b) 2

3 –4

c) 5 0

d) 3

2− 3

6. Find the slope and y-intercept of each line, if they exist. Graph each line.

a) y = 1

23x− +

b) y = x – 4 c) y = 5

d) y = 2

x−

6.2 - Practice: The Equation of a Line in Standard Form: Ax + By + C = 0

1. Rearrange each equation to isolate the variable indicated. Which step did you perform first each time?

a) d = st for t b) P = 6s for s c) A = P + I for P d) x + y = 4 for y

2. Express each equation in

the form y = mx + b.

a) x + y + 6 = 0 b) 2x + y = 0 c) 5x + y – 3 = 0 d) x + y – 1 = 0

3. Isolate the y term, then write each

equation in the form y = mx + b.

a) x + 3y + 1 = 0 b) 4x + 2y – 3 = 0 c) x + 3y = 0 d) 5x – y – 1 = 0 e) 6x – 5y + 1 = 0 f) 4x + 2y = 0

4. Write each equation in slope y-intercept form.

a) 7x + y – 4 = 0 b) 3x + 2y – 8 = 0 c) x – 4y – 2 = 0 d) 4x – 3y = 0

5. Identify the slope and y-intercept of

each line.

a) x – 2y + 6 = 0 b) 3x + 2y – 1 = 0 c) 3x + 8y + 16 = 0 d) x – y = 0

6. Use the slope and y-intercept to graph

each line from question 5.

6.3 - Practice: Graph a Line Using Intercepts

1. Identify the x- and y-intercept of each line.

a)

b)

c)

d)

2. The x- and y-intercepts for some lines are given. Use the intercepts to graph the line. a) x-intercept: 3 y-intercept: –1 b) x-intercept: –2 y-intercept: –3 c) x-intercept: 6 y-intercept: 1 d) x-intercept: 3 y-intercept: none

3. Use the graph to find the slope of each

line in question 2. 4. Identify the x- and y-intercepts of each

line. a) 3x – y = 4 b) 5x + 2y – 3 = 0 c) x + 3y = 6 d) x – 6y = 3

6.4 - Practice: Parallel and Perpendicular Lines

1. Graph each pair of lines on the same grid. Find the slope of each line. State whether the lines are parallel, perpendicular, or neither.

a) y = 1

3x + 2 y = 1

3x – 1

b) y = 4

5x + 3 y = 4

5− x

c) y = 2x – 4 2x – y = 3

d) x – 4y + 2 = 0 y = –4x + 1 2. The slopes of pairs of lines are given. Are

the lines in each pair parallel, perpendicular, or neither?

a) m = 2

3 m = 3

2

b) m = 1 m = –1

c) m = –2 m = –2

d) m = –3 m = 1

3

e) m = 2

5

− m = 2

5−

f) m = 3

4− m = 3

4

g) m = 4

5 m = 0.8

h) m = 3

8 m = 2

32−

3. Find the slope of each line. Are the lines in each pair parallel, perpendicular, or neither?

a) y = 1

4x + 4 y =

4

x

b) y = 3

5x + 2 y = 4

5x – 2

c) 0 = 3x – y + 5 y = –3x – 1

d) x – 6y + 24 = 0 6x + y = 0

e) y = 3x + 4 6x – 2y = 10

f) x – y = 5 x + y = 1

4. What is the slope of a line that is parallel to each line?

a) y = 2x + 1

b) 5x + y – 3 = 0

c) x – 3y = 4

d) y + 3 = 4x

5. What is the slope of a line that is perpendicular to each line?

a) y = 3

7x – 3

b) 2x – 4y + 1 = 0

c) y = 2x

d) 6 – x + 2y = 0

6. Write the equation of a line that is parallel to 4x + 3y = 1.

7. Write the equation of a line that is

perpendicular to x – 5y = 2.

6.5 - Practice: Find an Equation for a Line Given the Slope and a Point

1. The slope and a y-intercept are given for different lines. Find the equation of each line.

a) m = 5 b = 2

b) m = 3 b = –4

c) m = –2 b = 0

d) m = 4 b = 8

e) m = –6 b = –1

f) m = 3

4− b = 12

g) m = 2

3 b = –5

h) m = 1

5 b = –2

2. The slope and a point on a line are given

for different lines. Find the equation of each line.

a) m = 1 P(0, 3)

b) m = –1 P(4, 0)

c) m = 2 P(1, 1)

d) m = –3 P(–4, 2)

e) m = 1

5 P(10, 4)

f) m = 1

4− P(–4, –1)

g) m = 2

5 P(–10, 3)

h) m = 1

8 P(6, 0)

3. Find the equation of a line

a) with slope 4, passing through (1, 1)

b) with slope –1, passing through (5, 0)

c) with slope 1

2, passing through (8, 2)

d) parallel to a line with slope 5, and through (–1, 6)

e) perpendicular to a line with slope 2, and through (2, 5)

f) perpendicular to y = 1

5x, and through

the origin

g) parallel to 3y = 6x, and through (–2, 3)

h) perpendicular to y – x = 1, and through (3, 3)

4. A line passes through (2, 5) and (4, 0).

a) Use the coordinates of the two points on the line to find the slope.

b) Use the slope from part a) and one of the points to find the y-intercept.

c) Write an equation of the line.

6.6 - Practice: Find an Equation for a Line Given Two Points

1. Find the slope of the line that passes through each pair of points.

a) A(2, 3) and B(4, 5)

b) M(0, 6) and N(2, 0)

c) S(8, 7) and T(0, 0)

d) C(3, 4) and D(6, 7)

e) P(5, 1) and Q(4, 5)

f) E(2, 3) and F(4, 5)

g) V(–1, 1) and W(2, –4)

h) J(2, –1) and K(1, –2)

2. Find an equation for each line.

a)

b)

c)

3. Find an equation for the line that passes through each pair of points.

a) C(4, 5) and D(5, 1)

b) J(3, 2) and K(1, 0)

c) G(7, 7) and H(0, 4)

d) S(–3, 1) and T(–2, 7)

e) P(4, 5) and Q(2, 3)

f) M(–3, 3) and N(3, –5)

g) X(0, –1) and Z(5, –4)

h) A(4, –1) and B(–2, –2)

4. A line has an x-intercept of 3

and a y-intercept of 4.

a) Find the slope of the line.

b) Write an equation for the line.

5. A line passes through the origin

and A(4, 6).

a) Find the slope of the line.

b) Write an equation for the line.

6.7 - Practice: Linear Systems

1. What are the coordinates of the point of intersection of each linear system?

a)

b)

2. What is the solution to each linear system?

a)

b)

3. Solve each linear system. Check your solution in both equations.

a) x + y = 4 and y = x

b) 2x + y = 8 and y = 2x

c) 3x + y = 1 and y = 3x + 7

d) x + y = 3 and x – y = –1

4. Which is the point of intersection for the linear system y = 2x + 1 and y = 3x – 1?

A (2, 2)

B (2, 5)

C (5, 2)

D (5, 5)

5. Which is the solution to the linear system

y = 2x – 2 and y = 1

4− x + 7?

A (4, 1)

B (4, –6)

C (4, 6)

D (4, –1)

Chapter 6 Review

6.1 The Equation of a Line in Slope

y-Intercept Form: y = mx + b,

pages 296–307

1. Find the slope and y-intercept of each line.

a)

b)

2. Identify the slope and y-intercept of each line. a) y = 4x – 5

b) y = 1

6− x + 2

3. Write the equation of a line with each

slope and y-intercept. Then, graph each line. a) m = –1, b = 0

b) m = 2

3, b = 5

6.2 The Equation of a Line in Standard

Form: Ax + By + C = 0, pages 308–314

4. Express each equation in the form y = mx + b.

a) 6x – y = 4 b) x + 4y = 28

5. Identify the slope and y-intercept of each equation.

a) 8x + y = 4 b) –3x + 2y = 8

6.3 Graph a Line Using Intercepts,

pages 315–322

6. Identify the x- and y-intercepts of each line. Then, graph the line

a) 4x – 2y = 8 b) x + 3y = 6 c) 2x – y = 4 d) 5x + 3y – 15 = 0

6.4 Parallel and Perpendicular Lines,

pages 326–329

7. Which lines are parallel? 2x – 3y + 12 = 0 3y = 2x + 6 3x – 2y = 0 3x + 2y = –4

8. Which lines in question 7 are perpendicular?

9. What is the slope of a line that is perpendicular to 3 – x + 4y = 0?

6.5 Find an Equation for a Line Given the

Slope and a Point, pages 330–337

10. Find the equation of a line with a slope of –3, passing through (2, –5).

11. Find the equation of a line parallel to 2x + 5y = 1, with the same y-intercept as x – 4y = 8.

Chapter 6 Practice Test

Multiple Choice

For each question, select the best answer. 1. Which are the slope and y-intercept of the

line y = 5x + 3?

A m = 3, b = 5

B m = –3, b = –5

C m = –5, b = 3

D m = 5, b = 3

2. What are the x- and y-intercepts of the line

5x – 4y = 20?

A x-intercept = 4, y-intercept = –5

B x-intercept = –4, y-intercept = –5

C x-intercept = –4, y-intercept = 5

D x-intercept = 4, y-intercept = 5

3. What is the slope of a line parallel to x + 2y = 4?

A 2 B –2

C 1

2 D 1

2−

4. What is the slope of a line perpendicular to x + 2y = 4?

A 2 B –2

C 1

2 D 1

2−

5. Which is the solution to the linear system y = 6 – x and y = x – 4?

A (1, 5) B (5, 1)

C (–1, 5) D (–5, –1) Short Response

6. Rearrange x – 2y + 4 = 0 into the form y = mx + b.

7. Erynn used a motion sensor to create this distance-time graph.

a) Find the slope and d-intercept. What information does each of these give us about Erynn’s motion?

b) Write an equation that describes this distance-time relationship.

8. Find an equation for a line

a) with slope –1 passing through (2, 2) b) that passes through (10, 3) and (5, 6)

Extend

Show all your work.

9. A line is perpendicular to x + 3y – 4 = 0 and has the same y-intercept as 2x + 5y – 20 = 0. Find an equation for the line.

10. A fitness club offers two membership

plans. Plan A: $30 per month Plan B: $18 per month plus $2 for each visit to the club a) Graph the linear system. When would

the cost of the two membership plans be the same?

b) Describe a situation under which you would choose each plan.

Chapter 6 Test

Multiple Choice

For each question, select the best answer.

1. Which are the slope and y-intercept of the line y = –x – 4?

A m = 0, b = –4 B m = 0, b = 4 C m = 1, b = 4 D m = –1, b = –4

2. What are the x- and y-intercepts of the line 3x + 2y = 12?

A x-intercept = 4, y-intercept = –6 B x-intercept = –4, y-intercept = –6 C x-intercept = –4, y-intercept = 6 D x-intercept = 4, y-intercept = 6

3. What is the slope of a line parallel to 4x + 2y = 7?

A 2 B –2

C 1

2 D 1

2−

4. What is the slope of a line perpendicular to 2x – y = 3?

A 2 B –2

C 2

1 D

2

1−

5. Which is the solution to the linear system y = 2x and y = x + 4?

A (4, 1) B (4, –2) C (4, 8) D (4, 4)

Short Response

6. Rearrange 8x + 2y + 11 = 0 into the form y = mx + b.

7. Frank recorded his motion with a motion sensor and produced this graph.

a) How far was Frank from the motion sensor when he started moving?

b) Was Frank moving toward the motion sensor or away from it? How fast was he moving?

c) Write an equation that describes this distance-time relationship.

8. Find an equation for a line

a) with slope 6 passing through (–1, 4) b) that passes through (–5, 0) and (5, 6)

Extend Show all your work. 9. A line is parallel to 5x + 2y – 8 = 0 and has

the same y-intercept as x + 4y – 12 = 0. Find an equation for the line.

10. A retail store offers two different hourly compensation plans: Plan A: $9.00 per hour Plan B: $7.50 per hour worked plus a $4.50 shift bonus. a) Graph the linear system. When would

the earnings from the two plans be the same?

b) Describe a situation under which you would choose each plan.

ANSWERS

6.1 Practice: The Equation of a Line in Slope y-Intercept Form: y = mx + b

1. Equation Slope y-Intercept

a) y = 4x + 1 4 1

b) y = 2

x − 3

1

2 −3

c) y = −2x −2 0

d) y = −x + 2 −1 2

2. a) −3; 6

b) 1

2; 2

c) 2

5− ; −2

d) 3

5; 3

3. a) y = −3x + 6

b) y = 1

2x + 2

c) y =2

5− x − 2

d) y = 3

5x + 3

4. a) y = x − 3

b) y = −6x + 6

5. a) y = −2x + 1

b) y = 2

3x − 4

c) y = 5x

d) y = 3

2− x + 3

6. a) slope 1

2− ; y-intercept 3

b) slope 1; y-intercept −4

c) slope 0; y-intercept 5

d) slope 1

2− ; y-intercept 0

6.2 Practice: The Equation of a Line in Standard Form: Ax + By + C = 0

1. a) =d

ts

b) =6

Ps

c) P = A − I d) y = 4 − x

2. a) y = −x − 6

b) y = −2x

c) y = −5x + 3

d) y = −x + 1

Answers

3. a) 3y = −x − 1; 1 1

=3 3

y x− −

b) 2y = −4x − 3; y = −2x + 3

2

c) 3y = −x; 1

=3

y x−

d) y = 5x − 1

e) 5y = 6x + 1; 6 1

=5 5

y x +

f ) 2y = −4x; y = −2x

4. a) y = −7x + 4 b) 3

42

y x= − +

c) 1 1

=4 2

y x − d) 4

=3

y x

5. a) 1

2; 3 b)

3

2− ;

1

2

c) 8

3− ; −2 d) 1; 0

6. a)

b)

c)

d)

6.3 Practice: Graph a Line Using Intercepts

1. a) x-intercept: 3; y-intercept: −2

b) x-intercept: −3; y-intercept: −4 c) x-intercept: 2; y-intercept: 4

d) x-intercept: −6; y-intercept: −2

2. a)

b) c)

d)

3. a) 1

3 b)

3

2−

c) 1

6− d) undefined

4. a) x-intercept: 4

3; y-intercept: −4

b) x-intercept: 3

5; y-intercept:

3

2

c) x-intercept: 6; y-intercept: 2

d) x-intercept: 3; y-intercept: 1

2−

6.4 Practice: Parallel and Perpendicular Lines

1. a)

parallel b)

neither

c)

parallel

d)

perpendicular

2. a) neither b) perpendicular c) parallel d) perpendicular e) parallel f ) neither g) parallel h) perpendicular

3. a) 1 1

,4 4

; parallel

b) 3 4

,5 5

; neither

c) 3, −3; neither

d) 1

, 66

− ; perpendicular

e) 3, 3; parallel

f ) 1, −1; perpendicular

4. a) 2 b) −5

c) 1

3 d) 4

5. a) 7

3− b) −2

c) 1

2− d) −2

6. Possible answer: 4= 5

3y x− +

7. Possible answer: y = −5x

Answers

6.5 Practice: Find an Equation for a Line Given the Slope and a Point

1. a) y = 5x + 2

b) y = 3x − 4

c) y = −2x d) y = 4x + 8

e) y = −6x − 1

f ) y = 3

4− x + 12

g) y = 2

3x − 5

h) y = 1

5x − 2

2. a) y = x + 3

b) y = −x + 4

c) y = 2x − 1

d) y = −3x − 10

e) y = 1

5x + 2

f ) y = 1

4− x − 2

g) y = 2

5x + 7

h) y = 1

8x −

3

4

3. a) y = 4x − 3

b) y = −x + 5

c) y = 1

2x − 2

d) y = 5x + 11

e) y = 1

2− x + 6

f ) y = −5x g) y = 2x + 7

h) y = −x + 6

4. a) 5

2−

b) 10

c) y = 5

2− x + 10

6.6 Practice: Find an Equation for a Line Given Two Points

1. a) 1 b) −3

c) 7

8 d) 1

e) −4 f ) 1

g) 5

3− h) 1

2. a) 1

= 32

y x −

b) y = 3x + 1

c) y = −2x + 6

3. a) y = −4x + 21 b) y = x − 1

c) 3

= 47

y x + d) y = 6x + 19

e) y = x + 1 f ) 4

= 13

y x− −

g) 3

= 15

y x− − h) 1 5

=6 3

y x −

4. a) 4

3− b)

4= 4

3y x− +

5. a) 3

2 b)

3=

2y x

6.7 Practice: Linear Systems

1. a) (3, 2) b) (−1, 4)

2. a) (1, 3) b) (4, −1) 3. a) (2, 2) b) (2, 4)

c) (−1, 4) d) (1, 2) 4. B 5. C

Chapter 6 Review

1. a) slope: −2; y-intercept: 6

b) slope: 3

2− ; y-intercept: −3

2. a) slope: 4; y-intercept: −5

b) slope: 1

6− ; y-intercept: 2

3. a) y = −x

b) y = 2

3x + 5

4. a) y = 6x − 4

b) = 74

xy − +

5. a) slope: −8; y-intercept: 4

b) slope: 3

2; y-intercept: 4

6. a) x-intercept: 2; y-intercept: −4

b) x-intercept: 6; y-intercept: 2

c) x-intercept: 2; y-intercept: −4

d) x-intercept: 3; y-intercept: 5

7. 2x − 3y + 12 = 0 and 3y = 2x + 6

8. 2x − 3y + 12 = 0 and 3x + 2y = −4; 3y = 2x + 6 and

3x + 2y = −4

9. −4

10. y = −3x + 1

11. 2

= 25

y x− −

12. y = −9x + 23

13. a) −1.1

b) d = −1.1t + 5

c) About 4.5 s

14. (1, 1)

15. (2, 4)

Chapter 6 Practice Test

1. D 2. A 3. D 4. A 5. B

6. 1

= 22

y x +

7. a) slope: −1.2; d-intercept: 12

b) d = −1.2t + 12 8. a) = 4y x− +

b) 3

= 95

y x− +

Answers

9. = 3 4y x +

10. a)

When you make 6 visits per month, the cost for both plans is $30.

b) I would choose Plan A if I go to the gym more than 6 times each month. If I thought I would

go fewer than 6 times per month, I would choose Plan B (or not get a membership!).

Chapter 6 Test

1. D 2. D 3. B 4. D 5. C

6. 11

= 42

y x− −

7. a) 3 m b) Away; approximately 2.1 m/s c) d = 2.1t + 3

8. a) y = 6x + 10

b) 3

= 35

y x +

9. 5

= 32

y x− +

10. a) The earnings per shift under both plans are $27 when you work 3 h.

b) I would choose Plan A if I usually work more than 3 h each shift. If I work fewer than 3 h

per shift, I would