College algebra 9th edition ron larson test bank

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2.1 Linear Equations in Two Variables
1. Estimate the slope of the line.
y
5
4
3
2
1
–5

–4

–3

–2

–1
–1

1

2

3

4

x

5

–2
–3
–4
–5

a.
b.
c.
d.
e.

1.5
4.5
2.5
3.5
Undefined

ANS: A

PTS: 1

REF: 2.1.13

2. Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line.

a.

d.
y

–5

b.

–4

–3

–2

y

5

5

4

4

3

3

2

2

1

1

–1
–1

1

2

3

4

5

x

–5

–4

–3

–2

–1
–1

–2

–2

–3

–3

–4

–4

–5

–5

7
y-intercept: (0, 5)

–5
y-intercept: (0, 5)
e.

1

2

3

4

5

x

y

–5

–4

–3

–2

y

5

5

4

4

3

3

2

2

1

1

–1
–1

1

2

3

4

5

x

–5

–4

–3

–2

–1

–1

–2

–2

–3

–3

–4

–4

–5

–5

–7
y-intercept: (0, 5)

m is undefined.
y-intercept: (0, 5)

1

2

3

4

5

x

c.
y
5
4
3
2
1
–5

–4

–3

–2

–1
–1

1

2

3

4

5

x

–2
–3
–4
–5

5
y-intercept: (0, 5)
ANS: A

PTS: 1

REF: 2.1.17

3. Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line.

a.

d.

y

–5

–4

–3

–2

y

5

5

4

4

3

3

2

2

1

1

–1
–1

1

2

3

4

5

x

–5

–4

–3

–2

–1
–1

–2

–2

–3

–3

–4

–4

–5

–5

5
y-intercept: (0, 5)

–5
y-intercept: (0, 5)

b.

1

2

3

4

5

x

1

2

3

4

5

x

e.
y

–5

–4

–3

–2

y

5

5

4

4

3

3

2

2

1

1

–1
–1

1

2

3

4

5

x

–5

–3

–4

–4

–5

–5

m is undefined.
y-intercept: (0, 5)

5
4
3
2
1
–2

–1
–1

1

2

3

4

5

x

–2
–3
–4
–5

–1
y-intercept: (0, 5)
ANS: B

–1
–1

–3

y

–3

–2

–2

c.

–4

–3

–2

1
y-intercept: (0, –5)

–5

–4

PTS: 1

REF: 2.1.18

4. Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line.

a.

d.
y

–10 –8

–6

–4

y

10

10

8

8

6

6

4

4

2

2

–2
–2

2

4

6

8

10

x

–10 –8

–6

–4

–2
–2

–4

–4

–6

–6

–8

–8

–10

–10

2

4

6

8

10

x

2

4

6

8

10

x

m is undefined.
y-intercept: (0, 4)

y-intercept: (0, 4)
b.

e.
y

–10 –8

c.

–6

–4

y

10

10

8

8

6

6

4

4

2

2

–2
–2

2

4

6

8

10

x

–10 –8

–6

–4

–2
–2

–4

–4

–6

–6

–8

–8

–10

–10

–1
y-intercept: (0, 6)

6
y-intercept: (0, 6)

y
10
8
6
4
2
–10 –8

–6

–4

–2
–2

2

4

6

8

10

x

–4
–6
–8
–10

–6
y-intercept: (0, 6)
ANS: D

PTS: 1

REF: 2.1.19

5. Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line.

a.

d.
y

–5

–4

–3

–2

y

5

5

4

4

3

3

2

2

1

1

–1
–1

1

2

3

4

5

x

–5

–3

–2

–1
–1

–2

–2

–3

–3

–4

–4

–5

–5

–3
y-intercept: (0,5)

m is undefined.
There is no y-intercept.
b.

–4

e.

1

2

3

4

5

x

y

–5

–4

–3

–2

y

5

5

4

4

3

3

2

2

1

1

–1
–1

1

2

3

4

5

x

–5

–4

–3

–2

–1
–1

–2

–2

–3

–3

–4

–4

–5

–5

m is undefined.
There is no y-intercept.

1

2

3

4

5

x

m is undefined.
There is no y-intercept.

c.
y
5
4
3
2
1
–5

–4

–3

–2

–1
–1

1

2

3

4

5

x

–2
–3
–4
–5

–5
y-intercept: (0,3)
ANS: B

PTS: 1

REF: 2.1.21

6. Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line.

a.

d.

y

y

–5

–4

–3

–2

5

5

4

4

3

3

2

2

1

1

–1
–1

1

2

3

4

5

x

–5

–4

–3

–2

–1
–1

–2

–2

–3

–3

–4

–4

–5

–5

m is Undefined.

0

8
y-intercept: (0,  )
5

8
y-intercept: (0, )

5

b.

1

2

3

4

5

x

1

2

3

4

5

x

e.
y

–5

–4

–3

–2

y

5

5

4

4

3

3

2

2

1

1

–1
–1

1

2

3

4

5

x

–1
–1

–3

–4

–4

–5

–5

There is no y-intercept.

y

4
3
2
1
–2

–2

–3

5

–3

–3

–2

c.

–4

–4

–2

–5
y-intercept: (0, 8)

–5

–5

–1
–1
–2
–3
–4
–5

–8
y-intercept: (0, 5)

1

2

3

4

5

x

ANS: D

PTS: 1

REF: 2.1.22

7. Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line.

a.

d.
y

y

7

7

6

6

5

5

4

4

3

3

2

2

1

1

–7 –6 –5 –4 –3 –2 –1
–1

1

2

3

4

5

6

7

x

–7 –6 –5 –4 –3 –2 –1
–1

–2

–2

–3

–3

–4

–4

–5

–5

–6

–6

–7

–7

–3
y-intercept: (0, 7)

0
y-intercept: (0, 7)

b.

2

3

4

5

6

7

x

1

2

3

4

5

6

7

x

e.
y

y

7

7

6

6

5

5

4

4

3

3

2

2

1

1

–7 –6 –5 –4 –3 –2 –1
–1

1

2

3

4

5

6

7

x

–7 –6 –5 –4 –3 –2 –1
–1

–2

–2

–3

–3

–4

–4

–5

–5

–6

–6

–7

–7

–7
y-intercept: (0, 3)
c.

1

m is Undefined.
7
y-intercept: (0,  )
3

y
7
6
5
4
3
2
1
–7 –6 –5 –4 –3 –2 –1
–1

1

2

3

4

5

6

7

x

–2
–3
–4
–5
–6
–7

There is no y-intercept.
ANS: D

PTS: 1

REF: 2.1.25

8. Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line.

a.

d.
y

–5

–4

–3

–2

y

5

5

4

4

3

3

2

2

1

1

–1
–1

1

2

3

4

5

x

–5

–3

–2

–1
–1

–2

–2

–3

–3

–4

–4

–5

–5

m is Undefined.
There is no y-intercept.
b.

–4

0
y-intercept: (0,–5)
e.

1

2

3

4

5

x

y

y

–5

–4

–3

–2

5

5

4

4

3

3

2

2

1

1

–1

–1

1

2

3

4

5

x

–5

–4

–3

–2

–1
–1

–2

–2

–3

–3

–4

–4

–5

–5

0
y-intercept: (0,–5)

1

2

3

4

5

x

There is no y-intercept.

c.
y

5
4
3
2
1
–5

–4

–3

–2

–1
–1

1

2

3

4

5

x

–2
–3

–4
–5

0
y-intercept: (0,5)
ANS: D

PTS: 1

REF: 2.1.26

9. Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line.

a.

d.

y

–5

–4

–3

–2

y

5

5

4

4

3

3

2

2

1

1

–1
–1

1

2

3

4

5

x

–5

–4

–3

–2

–1
–1

–2

–2

–3

–3

–4

–4

–5

–5

m is undefined.
There is no y-intercept.

1

2

3

4

5

x

2

3

4

5

x

m is undefined.
There is no y-intercept.

b.

e.
y

–5

–4

–3

–2

y

5

5

4

4

3

3

2

2

1

1

–1
–1

1

2

3

4

5

x

–5

–3

–4

–4

–5

–5

4
3
2
1
–1
–1

1

2

3

4

5

x

–2
–3
–4
–5

–4
y-intercept: (0,3)
ANS: D

1

m is undefined.
There is no y-intercept.

5

–2

–1
–1

–3

y

–3

–2

–2

c.

–4

–3

–2

–3
y-intercept: (0,4)

–5

–4

PTS: 1

REF: 2.1.27

10. Plot the points and find the slope of the line passing through the pair of points.

(0, 6), (4, 0)
a.

d.
y

–10 –8

–6

–4

y

10

10

8

8

6

6

4

4

2

2

–2
–2

2

4

6

8

10

x

–10 –8

–6

–4

–2
–2

–4

–4

–6

–6

–8

–8

–10

–10

3
4

–

b.

4

6

8

10

x

2

4

6

8

10

x

2
3

e.
y

–10 –8

–
c.

2

3
2

–6

–4

y

10

10

8

8

6

6

4

4

2

2

–2
–2

2

4

6

8

10

x

–10 –8

–6

–4

–2
–2

–4

–4

–6

–6

–8

–8

–10

–10

3
2

y
10
8
6
4
2
–10 –8

–6

–4

–2
–2

2

4

6

8

10

x

–4
–6
–8
–10

–

3
2

ANS: B

PTS: 1

REF: 2.1.29

11. Plot the points and find the slope of the line passing through the pair of points.

(11, 0), ( 0, –9)
a.

d.
y

y

15

15

12

12

9

9

6

6

3

3
(11, 0)

–15 –12 –9 –6 –3
–3

3

6

9

12 15

(11, 0)
x

–15 –12 –9 –6 –3
–3

–6
–9

–
b.

3

–6
–9

(0, –9)

–12

–12

–15

–15

11
9

11
9
e.

(0, –9)

6

9

12 15

x

y

y
15

15

12

12

9

9

6

6
3

3
(–7, 0)

(11, 0)
–15 –12 –9 –6 –3
–3

3

6

9

12 15

x

–15 –12 –9 –6 –3
–3

3

6

9

–6

–6
–9

(0, 13)

–9

(0, –9)

–12

–12

–15

–15

9
11



7
13

c.
y
15
12

(0, 11)

9
6
3
(–9, 0)
–15 –12 –9 –6 –3
–3

3

6

9

12 15

x

–6
–9
–12
–15

–

9
11

ANS: B

PTS: 1

REF: 2.1.30

12. Plot the points and find the slope of the line passing through the pair of points.

(–2, –9), ( 3, 5)
a.

d.

12 15

x

y

y

15

15

12

12

9

9

6

(4, 6)

6

(3, 5)

3

3

–15 –12 –9 –6 –3
–3

3

6

9

12 15

x

–15 –12 –9 –6 –3
–3

–6

–6

(–2, –9) –9

(–1, –8)–9

–12

–12

–15

–15

4

–

b.

3

6

9

12 15

x

14
5

e.
y

y

15

15

12

12

9

9

6

6

(3, 5)

3

3

–15 –12 –9 –6 –3
–3

3

6

9

12 15

x

–15 –12 –9 –6 –3
–3
(–18, –4)

–6

–9

–12

–12

–15

–15

14
5

5
14

c.

y
15
12

(7, 12)

9
6
3

(–18, –4)

3

6

9

12 15

x

–6
–9
–12
–15

–

5

14

ANS: B

–6

(–2, –9) –9

–15 –12 –9 –6 –3
–3

(7, 12)

PTS: 1

REF: 2.1.31

3

6

9

12 15

x

13. Plot the points and find the slope of the line passing through the pair of points.

(9, –4), ( 1, –4)
a.

y

d.
y

15

15

12

12

9

9

6

6

3

3
–15 –12 –9 –6 –3
–3
–15 –12 –9 –6 –3

–3
–6

3

6

9

(1, –4)

12 15

x

3

9

(1, –4)

–6

(9, –4)

6

x

12 15

(9, –4)

–9

–9

–12

–12

–15

–15

m
is undefined

0
b.

e.
y

y

15

15

12

12

9

9

6

6

3

3
(9, 0)

–15 –12 –9 –6 –3
–3
–6

–
c.

1
9

3
(1, –4)

6

9

12 15

x

–15 –12 –9 –6 –3
–3

(9, –4)

–6

–9

–9

–12

–12

–15

–15

1
9

3

(0, –4)

6

9

12 15

x

y
15
12
9
6
3
–15 –12 –9 –6 –3
–3
–6

3

6

9

(1, –4)

12 15

x

(9, –4)

–9
–12
–15



4
5

ANS: A

PTS: 1

REF: 2.1.33

14. Plot the points and find the slope of the line passing through the pair of points.

(4, 8), ( 8,–8)
a.

d.
y

y

15

15

12
9
6

6
3

3

6

9

12 15

x

–15 –12 –9 –6 –3
–3

–6

–6

–9

–9

–12

–12

–15

–15

4
b.

(12, 11)

9

(2, 8)

3
–15 –12 –9 –6 –3
–3

(8, 12)

12
(5, 9)

3
e.

3

6

9

12 15

x

y

y
15

15

12

12

9
6

6

3

3
3

6

(8, 12)

9

(4, 8)

–15 –12 –9 –6 –3
–3

(12, 12)

9

x

12 15

–15 –12 –9 –6 –3
–3

3

6

9

–6

–6
(8, –8)

–9

–9

–12

–12

–15

–15

4

3

c.
y
15
12
(4, 8)

9
6

(1, 7)

3
–15 –12 –9 –6 –3
–3

3

6

9

x

12 15

–6
–9
–12
–15

3
ANS: B

PTS: 1

REF: 2.1.32

15. Plot the points and find the slope of the line passing through the pair of points.

(0, –9), (–6, 0)
y

a.

d.

10
8
6
4
2
(–6, 0)
–10 –8

–6

–4

–2
–2

2

–4
–6
–8
–10

(0, –9)

4

6

8

10

x

12 15

x

y

3
2

10
8
6
4
2
(–8, 0)
–10 –8

–6

–4

–2
–2

2

4

6

8

10

x

4

6

8

10

x

–4
–6

–8
–10
(0, –11)

4
7
b.

e.
y

y

10

10

8

8

6

6

4

4

2

2

(–9, 0)
–10 –8

(–6, 0)
–6

–4

–2
–2

2

4

6

8

10

x

–10 –8

–4
–6

–8

–8

–10

–10

3
2

c.
y
10
8
6
4
2
(–9, 0)
–4

–2
–2

2

4

6

8

10

x

–4
–6

(0, –6)

–8
–10

–

3
2

ANS: E

–2
–2

2

–6

(0, –6)

–

–6

–4

–4

3
2

–10 –8

–6

PTS: 1

REF: 2.1.36

(0, –9)

16. Plot the points and find the slope of the line passing through the pair of points.

(4.1, 3.1), ( –2.8, 4.1)
a.

d.
y

(–1.8, 5.1)

y

15

15

12

12

9

9

6

6
(–2.8, 4.1)

(5.1, 4.1)

3
–15 –12 –9 –6 –3
–3

3

6

9

12 15

x

3

(4.1, 3.1)

–15 –12 –9 –6 –3
–3

–6

–6

–9

–9

–12

–12

–15

–15

3

6

9

12 15

x

12 15

x

–0.14

0.26
b.

e.
y

y

15

15

12

12
(7.1, 8.1)

9

9

6

6

3

(–2.8, 4.1)

(8.1, 1.2)

–15 –12 –9 –6 –3
–3

3

6

9

12 15

x

3

–15 –12 –9 –6 –3
–3

–6

–6

–9

–9

–12

–12

–15

–15

–6.9

5.54

c.
y
15
12
(7.1, 8.1)

9
6
3
–15 –12 –9 –6 –3
–3
–6
–9
–12
–15

(8.1, 1.2)
3

6

9

12 15

x

(4.1, 3.1)
3

6

9

0.66
ANS: D

PTS: 1

REF: 2.1.39

17. Find the slope-intercept form of the equation of the line that passes through the given point

and has the indicated slope m. Sketch the line.
(0,–4),
a.

d.
y
10
8

y
10

6

8

4

6

2

4
–10 –8

2
–10 –8

–6

–4

–2
–2

2

4

6

8

10

–6

–4

–2
–2

2

4

6

8

x

10

–4

x

–6

–4

–8

–6

–10

–8
–10

b.

e.
y
10
8

y
10

6

8

4

6

2

4
–10 –8

2
–10 –8

–6

–4

–2
–2

4

6

8

10

x

–4

–2
–2
–4
–6

–4

–8

–6

–10

–8
–10

c.

2

–6

2

4

6

8

10

x

y
10
8
6
4
2
–10 –8

–6

–4

–2
–2

2

4

6

8

10

x

–4
–6
–8
–10

ANS: B

PTS: 1

REF: 2.1.51

18. Find the slope-intercept form of the equation of the line that passes through the given point

and has the indicated slope m. Sketch the line.

a.

d.
y
10
8

y

6

10

4

8

2

6
4

–10 –8

–6

–4

–2
–2

2

4

6

8

10

x

2

–4
–6

–10 –8

–6

–4

–2
–2

–8

–4

–10

–6
–8
–10

b.

e.

2

4

6

8

10

x

y

y

–10 –8

–6

–4

10

10

8

8

6

6

4

4

2

2

–2
–2

2

4

6

8

10

x

–10 –8

–6

–4

–2
–2

–4

–4

–6

–6

–8

–8

–10

–10

2

4

6

c.
y
10
8
6
4
2
–10 –8

–6

–4

–2
–2

2

4

6

8

10

x

–4
–6
–8
–10

ANS: D

PTS: 1

REF: 2.1.53

19. Find the slope-intercept form of the equation of the line that passes through the given point and has the
indicated slope m.Sketch the line.

a.

d.

8

10

x

y

–10 –8

–6

–4

y

10

10

8

8

6

6

4

4

2

2

–2
–2

2

4

6

8

10

x

–10 –8

–6

–4

–2
–2

–4

–4

–6

–6

–8

–8

–10

–10

b.

2

4

6

8

10

x

2

4

6

8

10

x

e.
y

–10 –8

–6

–4

y

10

10

8

8

6

6

4

4

2

2

–2
–2

2

4

6

8

10

x

–10 –8

–6

–4

–2
–2

–4

–4

–6

–6

–8

–8

–10

–10

c.
y
10
8
6
4
2
–10 –8

–6

–4

–2
–2

2

4

6

8

10

x

–4
–6
–8
–10

ANS: D

PTS: 1

REF: 2.1.54

20. Find the slope-intercept form of the equation of the line that passes through the given point

and has the indicated slope m. Sketch the line.

m is undefined.
a.

d.
y
10

y
10

8

8

6

6

4

4

2