Name:
Additional Exercises 4.1
Date:
Indicate the quadrant in which each of the points belong.
1. (–8, 10)
1. ____________________________
2. (25, –36)
2. ____________________________
3. (94, 71)
3. ____________________________
4. (–281, –165)
4. ____________________________
List the ordered pairs corresponding to each point.
y
B
4
E
A
2
—4 —2
2
—2 D
—4
C
4
x
F
5. A
5. ____________________________
6. B
6. ____________________________
7. C
7. ____________________________
8. D
8. ____________________________
9. E
9. ____________________________
10. F
10. ____________________________
Plot each point.
11. A (2, –5)
11.–14.
y
x
12. B (0, 2)
13. C (5, 0)
14. D (–2, 4)
Determine if each set of points is collinear.
15. {(1, –5), (–4, –1), (6, –9)}
15. ____________________________
16. {(–3, –6), (3, –4), (14, 0)}
16. ____________________________
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Additional Exercises 4.1 (cont.)
Name:
17. {(2, 5) , (2, 7) , (2, –3)}
17. ____________________________
18. Find u such that the points (–2, 3), (4, u), and (0, –1) are
18. ____________________________
collinear.
19. Determine if the ordered pair (5, –5) is a solution of 4x – 3y = –35.
19. ____________________________
20. Determine if the ordered pair (–1, 3) is a solution of 4x – 3y = 13.
20. ____________________________
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122
Name:
Additional Exercises 4.2
Date:
Find the missing coordinate in the solutions for 2x – 4y = 4.
1. (?, 1)
1. ____________________________
2. (2, ?)
2. ____________________________
3. (–4, ?)
3. ____________________________
Find the missing coordinate in the solutions for 3x – y = –7.
4. (?, 7)
4. ____________________________
5. (2, ?)
5. ____________________________
6. (–1, ?)
6. ____________________________
Graph by plotting points. Plot at least three points for each graph.
7. 4x + y = 5
7.
y
x
8. y = 2x – 3
8.
y
x
9. 2 y = x − 8
9.
y
x
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Additional Exercises 4.2 (cont.)
Name:
Graph each equation.
10. y = –4
10.
y
x
11. x = –3
11.
y
x
Graph using the x and y intercepts.
12. 2x + 3y = 6
12.
y
x
13. x – 2y = –6
13.
y
x
14. 3x – 4y = 0
14.
y
x
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Additional Exercises 4.2 (cont.)
Name:
Write the equation represented by the given graph.
15.
15. ____________________________
y
4
2
—4 —2
—2
2
4
x
—4
16.
16. ____________________________
y
4
2
—4 —2
—2
2
4
x
—4
Use the following information for questions 17–20.
The cost of renting a U-Drive truck is an initial charge of $120 plus $0.50 per mile.
17. Write an equation for cost, c, in terms of miles driven, m.
17. ____________________________
18. Graph the equation for 0 to 500 miles driven.
18.
y
x
19. Estimate the cost of driving 200 miles.
19. ____________________________
20. If the total cost is $260, estimate the miles driven.
20. ____________________________
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Name:
Additional Exercises 4.3
Date:
Find the slope of the line through the given points.
1. (0, 3) and (–9, 1)
1. ____________________________
2. (–1, 1) and (8, 4)
2. ____________________________
3. (8, 5) and (3, –5)
3. ____________________________
4. (8, –7) and (4, 1)
4. ____________________________
5. (7, 2) and (7, –4)
5. ____________________________
6. (4, 7) and (9, 8)
6. ____________________________
7. (–3, 4) and (7, –4)
7. ____________________________
8. (3, –2) and (–1, –2)
8. ____________________________
9. (0, 0) and (2, 10)
9. ____________________________
10. (–2, –6) and (3, –2)
10. ____________________________
11. (1, 0) and (0, –7)
11. ____________________________
By observing the vertical and horizontal change of the line between the two points indicated, determine the slope of
the line.
12.
12. ____________________________
y
4
2
—4 —2
—2
13.
2
4
x
13. ____________________________
y
4
—4 —2
—2
2
4
x
—4
14.
14. ____________________________
y
2
—4 —2
—2
2
4
x
—4
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126
Additional Exercises 4.3 (cont.)
15. ____________________________
y
15.
Name:
2
—4 —2
2
4
x
—6
16. ____________________________
y
16.
4
2
—4 —2
—2
2
4
x
—4
17. ____________________________
y
17.
4
—4 —2
2
2
4
x
—2
—4
18. Find u so that the line through (1, 4) and (5, 7) , is parallel to
the line through (–2, –3) and (u, 3).
18. ____________________________
19. Find u so that the line through (7, 3) and (2, 4) , is perpendicular to
the line through (6, u) and (7, 8).
19. ____________________________
20. Find u so that the line through (1, 2) and (–3, 2) , is perpendicular to
the line through (3, –2) and (u, 5).
20. ____________________________
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Name:
Additional Exercises 4.4
Date:
Find the slope and the y-intercept of the line represented by the given equation.
1. y = –x + 12
1. ____________________________
2. y = 7x
2. ____________________________
3. 9x – 3y = –81
3. ____________________________
4. 5x – 4y = 4
4. ____________________________
Graph using the slope and y-intercept.
5. y = x + 2
5.
y
x
6. y = –3x – 3
6.
y
x
7. 6x + 3y = 9
7.
y
x
Determine the equation of each line.
8.
8. ____________________________
y
4
2
—4 —2
—2
2
4
x
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Additional Exercises 4.4 (cont.)
9.
Name:
9. ____________________________
y
4
2
—4 —2
—2
10.
2
4
x
10. ____________________________
y
4
2
—4 —2
—2
2
4
x
—4
Determine if the two given lines are parallel, perpendicular, or neither.
11. 4x + 9y = –27
4
y = − x −9
9
11. ____________________________
12. y = –3x + 6
–3y + x = –2
12. ____________________________
13. 28x + 14y = –3
–14y + 28x = –3
13. ____________________________
14. 2y = 3x – 2
8x + 12y = –2
14. ____________________________
Write the equation of the line with the given properties in slope-intercept form.
15. Having slope 7 and y-intercept –2.
15. ____________________________
16. Having slope 5 and y-intercept –5.
16. ____________________________
17. With slope 1 passing through the point (2, 3).
17. ____________________________
18. With slope 4 passing through the point (3, 4).
18. ____________________________
19. Through (1, 6) and (5, –2).
19. ____________________________
20. Through (1, –7) and (4, 2).
20. ____________________________
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Name:
Additional Exercises 4.5
Date:
Graph each inequality.
1. x > –2
1.
y
x
2. y ≤ 4
2.
y
x
3. y ≥ x + 3
3.
y
x
4. y ≤ –x – 1
4.
y
x
5. y ≤ 5 x − 5
5.
y
x
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130
Additional Exercises 4.5 (cont.)
6. y ≤ –3x + 3
Name:
6.
y
x
7. x – y > 0
7.
y
x
8. 5x – y < –5
8.
y
x
9. 3x – 4y > –12
9.
y
x
10. 6x – 5y ≥ –30
10.
y
x
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131
Additional Exercises 4.5 (cont.)
11. 3x – 2y > –6
Name:
11.
y
x
12. 3x – y < –3
12.
y
x
Decide whether or not (3, 2) is a solution to each of the following.
13. 5x – 4y < 7
13. ____________________________
14. 5x – 4y ≤ 7
14. ____________________________
15. 5x – 4y > 7
15. ____________________________
16. 5x – 4y ≥ 7
16. ____________________________
Decide whether or not the given point is a solution to the given inequality.
17. 3x + 2y < 3
(–2, 5)
17. ____________________________
18. 5x – y ≥ 1
(1, 3)
18. ____________________________
19. 2x + 3y > 5
(1, 1)
19. ____________________________
20. 2x – 3y ≤ 4
(1, –2)
20. ____________________________
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Name:
Additional Exercises 4.6
Date:
Use the relation {(2, –3), (1, 5), (–1, –4)}for questions 1–3.
1. Give the domain of the relation.
1. ____________________________
2. Give the range of the relation.
2. ____________________________
3. Is the relation a function?
3. ____________________________
Use the relation {(4, –2), (3, 1), (2, –2)}for questions 4–6.
4. Give the domain of the relation.
4. ____________________________
5. Give the range of the relation.
5. ____________________________
6. Is the relation a function?
6. ____________________________
Use the relation {(–3, 3), (–3, –1), (–1, –4)} for questions 7–9.
7. Give the domain of the relation.
7. ____________________________
8. Give the range of the relation.
8. ____________________________
9. Is the relation a function?
9. ____________________________
Use the relation illustrated to answer questions 10–11.
Domain
—2
0
3
5
Range
1
0
—3
10. Construct a set of ordered pairs that represent the relation.
10. ____________________________
11. Determine if the relation is a function.
11. ____________________________
Use the vertical line test to determine if the relation is also a function.
12. ____________________________
y
12.
4
2
—4 —2
—2
2
4
x
—4
13. ____________________________
y
13.
4
2
—4 —2
2
4
x
—4
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Additional Exercises 4.6 (cont.)
y
14.
Name:
14. _____________________________
4
2
−4
2
4
x
−4
Evaluate f ( x) =
1 2
x + 6 at the values indicated.
2
15. f(–2)
15. ____________________________
16. f(–4)
16. ____________________________
Graph each function.
17. f(x) = x – 4
17.
y
x
18. f(x) = 4x – 1
18.
y
x
Decide if each graph represents a function.
19.
19. ____________________________
Words
Jose's Chart
12
10
8
6
4
2
0
1
2
3 4
Weeks
5
Yearly Rainfall
Inches
20.
40
30
20
10
0
20. ____________________________
‘00 ‘01 ‘02 ‘03 ‘04 ‘05
Year
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