Download Extra Practice Chapter 6

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.
d)
y-Intercept
Equation
Slope
a) y = 4x + 1
x
b)
y= –3
2
c) y = –2x
d) y = –x + 2
2. Find the slope and y-intercept of each line.
a)
3. Write the equation of each line in
question 2.
4. Write the equation of each line.
a)
b)
b)
c)
5. Write the equation of a line with each
slope and y-intercept.
a)
b)
c)
d)
Slope
–2
y-Intercept
1
2
3
–4
5
0
−3
3
2
6. Find the slope and y-intercept of each line,
if they exist. Graph each line.
a) y = − 1 x + 3
2
b) y = x – 4
c) y = 5
d) y = − x
2
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.
d)
a)
b)
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.
c)
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 x + 2
y= 1x–1
b) y = 4 x + 3
y = −4x
c) y = 2x – 4
d) x – 4y + 2 = 0
2x – y = 3
y = –4x + 1
3
5
3
5
2. The slopes of pairs of lines are given. Are
the lines in each pair parallel,
perpendicular, or neither?
a) m = 2
m= 3
b) m = 1
c) m = –2
m = –1
m = –2
d) m = –3
m= 1
e) m = −2
m= 2
f) m = − 3
m= 3
g) m = 4
m = 0.8
h) m = 3
m = −2 2
2
3
5
4
5
8
−5
4
3
y= x
b) y = 3 x + 2
y= 4x– 2
c)
d)
e)
f)
0 = 3x – y + 5
x – 6y + 24 = 0
y = 3x + 4
x–y=5
a) y = 3 x – 3
7
b) 2x – 4y + 1 = 0
c) y = 2x
d) 6 – x + 2y = 0
7. Write the equation of a line that is
perpendicular to x – 5y = 2.
3
a) y = 1 x + 4
5
5. What is the slope of a line that is
perpendicular to each line?
6. Write the equation of a line that is parallel
to 4x + 3y = 1.
3. Find the slope of each line. Are the lines
in each pair parallel, perpendicular, or
neither?
4
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
4
5
y = –3x – 1
6x + y = 0
6x – 2y = 10
x+y=1
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
b = 12
g) m = 2
b = –5
h) m = 1
b = –2
4
3
5
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
P(10, 4)
5
f) m = − 1
P(–4, –1)
g) m = 2
P(–10, 3)
h) m = 1
P(6, 0)
4
5
8
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 , passing through (8, 2)
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 x, and through
5
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 x + 7?
4
A
B
C
D
(4, 1)
(4, –6)
(4, 6)
(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)
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
b)
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
2. Identify the slope and y-intercept of
each line.
a) y = 4x – 5
b) y = − 1 x + 2
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
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 , b = 5
3
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
7. Erynn used a motion sensor to create this
distance-time graph.
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
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)
D −1
2
Extend
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.
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
7. Frank recorded his motion with a motion
sensor and produced this graph.
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?
B –2
A 2
1
C
D −1
2
2
4. What is the slope of a line perpendicular
to 2x – y = 3?
B –2
A 2
1
C
2
1
D −
2
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.
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.
a)
b)
c)
d)
2.
a)
b)
c)
d)
3.
a)
b)
c)
d)
Equation
y = 4x + 1
Slope
4
y= x −3
2
y = −2x
y = −x + 2
1
2
−2
−1
−3
0
2
c)
−3; 6
1;2
2
− 2 ; −2
5
3;3
5
y = −3x + 6
y= 1x+2
2
y =−2 x − 2
5
y= 3x+3
5
4.
a) y = x − 3
b) y = −6x + 6
5.
y = −2x + 1
b) y = 2 x − 4
3
c) y = 5x
d) y = − 3 x + 3
2
a) slope − 1 ; y-intercept 3
2
6.
y-Intercept
1
slope 0; y-intercept 5
d) slope − 1 ; y-intercept 0
2
a)
6.2 Practice: The Equation of
a Line in Standard Form: Ax +
By + C = 0
1.
2.
b) slope 1; y-intercept −4
t=d
s
c) P = A − I
a) y = −x − 6
b) y = −2x
c) y = −5x + 3
d) y = −x + 1
a)
b)
d)
s= P
6
y=4−x
Answers
a)
4.
a)
c)
5.
a)
c)
6.
d)
3y = −x − 1; y = − 1 x − 1
3
3
b) 2y = −4x − 3; y = −2x + 3
2
1
c) 3y = −x; y = − x
3
d) y = 5x − 1
e) 5y = 6x + 1; y = 6 x + 1
5
5
f ) 2y = −4x; y = −2x
3.
y = −7x + 4
y= 1x−
4
1;3
2
− 8 ; −2
3
1
2
b)
d)
b) y = − 3 x + 4
2
4
d) y = x
3
3
1
− ;
2 2
1; 0
6.3 Practice: Graph a Line
Using Intercepts
1.
a)
2.
a)
b)
c)
d)
a)
b)
b)
c)
c)
x-intercept: 3; y-intercept: −2
x-intercept: −3; y-intercept: −4
x-intercept: 2; y-intercept: 4
x-intercept: −6; y-intercept: −2
d)
3.
a)
c)
4.
c)
1
3
b) − 3
2
−1
6
d) undefined
parallel
d)
x-intercept: 4 ; y-intercept: −4
3
3
b) x-intercept: ; y-intercept: 3
2
5
c) x-intercept: 6; y-intercept: 2
d) x-intercept: 3; y-intercept: − 1
2
a)
6.4 Practice: Parallel and
Perpendicular Lines
1.
a)
perpendicular
2.
3.
parallel
b)
4.
5.
6.
7.
neither
a)
c)
e)
g)
neither
parallel
parallel
parallel
b)
d)
f)
h)
perpendicular
perpendicular
neither
perpendicular
1 , 1 ; parallel
4 4
3
b)
, 4 ; neither
5 5
c) 3, −3; neither
d) 1 , − 6 ; perpendicular
6
e) 3, 3; parallel
f ) 1, −1; perpendicular
a) 2
b) −5
1
c)
d) 4
3
a) − 7
b) −2
3
c) − 1
d) −2
2
Possible answer: y = − 4 x + 5
3
Possible answer: y = −5x
a)
Answers
6.5 Practice: Find an
Equation for a Line Given the
Slope and a Point
1.
a)
b)
c)
d)
e)
f)
g)
h)
2.
a)
b)
c)
d)
e)
f)
g)
h)
3.
a)
b)
c)
d)
e)
f)
g)
h)
4.
a)
b)
c)
y = 5x + 2
y = 3x − 4
y = −2x
y = 4x + 8
y = −6x − 1
y = − 3 x + 12
4
2
y= x−5
3
1
y= x−2
5
y=x+3
y = −x + 4
y = 2x − 1
y = −3x − 10
y= 1x+2
5
y= −1x−2
4
y= 2x+7
5
1
y= x− 3
4
8
y = 4x − 3
y = −x + 5
y= 1x−2
2
y = 5x + 11
y= −1x+6
2
y = −5x
y = 2x + 7
y = −x + 6
−5
2
10
y = − 5 x + 10
2
6.6 Practice: Find an
Equation for a Line Given
Two Points
1.
a)
c)
e)
g)
1
7
8
−4
−5
3
b) −3
d) 1
f) 1
h) 1
2.
3.
y= 1x−3
2
b) y = 3x + 1
c) y = −2x + 6
a) y = −4x + 21
c) y = 3 x + 4
7
a)
e)
y=x+1
y = − 3 x −1
5
a) − 4
3
3
a)
2
g)
4.
5.
b) y = x − 1
d) y = 6x + 19
f) y = − 4 x − 1
3
1
h) y = x − 5
6
3
b) y = − 4 x + 4
3
3
b) y = x
2
6.7 Practice: Linear Systems
1.
2.
3.
4.
5.
a)
a)
a)
c)
B
C
(3, 2)
(1, 3)
(2, 2)
(−1, 4)
b)
b)
b)
d)
(−1, 4)
(4, −1)
(2, 4)
(1, 2)
Chapter 6 Review
1.
2.
3.
slope: −2; y-intercept: 6
b) slope: − 3 ; y-intercept: −3
2
a) slope: 4; y-intercept: −5
b) slope: − 1 ; y-intercept: 2
6
a) y = −x
a)
b)
y= 2x+5
3
d) x-intercept: 3; y-intercept: 5
4.
5.
6.
y = 6x − 4
b) y = − x + 7
4
a) slope: −8; y-intercept: 4
b) slope: 3 ; y-intercept: 4
2
a)
a)
x-intercept: 2; y-intercept: −4
7.
8.
9.
10.
11.
12.
13.
b) x-intercept: 6; y-intercept: 2
14.
15.
2x − 3y + 12 = 0 and 3y = 2x + 6
2x − 3y + 12 = 0 and 3x + 2y = −4; 3y = 2x + 6 and
3x + 2y = −4
−4
y = −3x + 1
y=−2x−2
5
y = −9x + 23
a) −1.1
b) d = −1.1t + 5
c) About 4.5 s
(1, 1)
(2, 4)
Chapter 6 Practice Test
1.
2.
3.
4.
5.
6.
7.
c)
x-intercept: 2; y-intercept: −4
8.
D
A
D
A
B
y= 1x+2
2
a) slope: −1.2; d-intercept: 12
b) d = −1.2t + 12
a) y = − x + 4
b)
y=−3x+9
5
Answers
9.
10.
y = 3x + 4
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.
2.
3.
4.
5.
6.
7.
8.
9.
10. a)
D
D
B
D
C
y = − 4 x − 11
2
a) 3 m
b) Away; approximately 2.1 m/s
c) d = 2.1t + 3
y = 6x + 10
b) y = 3 x + 3
5
5
y=− x+3
2
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