Name: ________________________ Class: ___________________ Date: __________
ID: A
Algebra Unit 7 Review Packet
Short Answer
Solve the inequality. Then graph your solution.
1.
Graph the equation.
9. y + 2 = –(x – 4)
|d + 2| ≥ 6
2. | 2x + 9 | < 25
Solve the equation. If there is no solution, write
no solution.
3. | x | − 7 = 6
4. 2| n | − 12 = 16
10. y + 5 = −(x + 2)
5.
|| j ||
+1= −4
5
6. −2 |h − 7 | = − 28
2
7. Write y = x + 7 in standard form using integers.
3
8. Write an equation of a line that has the same slope
as 2x – 5y = 12 and the same y-intercept as
4y + 24 = 5x.
Write an equation in point-slope form for the
line through the given point with the given
slope.
11. (4, –6); m =
3
5
12. (10, –9); m = −2
1
Name: ________________________
ID: A
13. A line passes through (2, –1) and (8, 4).
a. Write an equation for the line in point-slope
form.
b. Rewrite the equation in standard form using
integers.
Are the graphs of the lines in the pair parallel?
Explain.
1
17. y = x + 8
6
–2x + 12y = –11
18. y = 5x + 6
–18x + 3y = –54
Is the relationship shown by the data linear? If
so, model the data with an equation.
Write an equation for the line that is parallel to
the given line and that passes through the given
point.
14.
x
y
–9
–2
–5
–7
–1
–12
3
–17
19. y = –5x + 3; (–6, 3)
3
20. y = x – 9; (–8, –18)
4
Tell whether the lines for each pair of equations
are parallel, perpendicular, or neither.
15.
x
y
3
1
7
2
11
3
18
5
21. 7x – 4y = 4
x – 4y = 3
1
22. y = − x – 11
2
16x – 8y = –8
Write the equation of a line that is
perpendicular to the given line and that passes
through the given point.
16. The table shows the height of a plant as it grows.
a. Model the data with an equation.
b. Based on your model, predict the height of the
plant at 12 months.
Time (months)
Plant Height (cm)
3
9
5
15
7
21
9
27
23. 4x – 12y = 2; (10, –1)
24. y =
2
2
x + 9 ; (–6, 5)
3
Name: ________________________
ID: A
25. The table shows the amount of time a student spends practicing each week and her typing speed.
Practice (hours)
1
2
3
4
5
Typing Speed (words per minute)
21
26
35
37
40
a. Graph the data and write the equation for the trend line.
b. Use your equation to predict the student’s typing speed if she spends 8 hours practicing each week.
Graph each equation by translating y = | x |.
26. Graph y = | x | – 5.
30. y = | x + 6 |
Write an equation for each translation of
y = |x | .
27. 2 units up
28. 6 units left
29. 16.5 units right
3
Name: ________________________
ID: A
33. Gloria makes and sells handmade greeting cards.
The scatter plot shows the number of cards she
made over a 10-hour period. Find the equation of a
trend line and use it to predict the number of cards
Gloria can make in 12 hours.
31. y = | x + 2 |
32. y = | x – 3 | – 4
Essay
5
34. Write y = x – 11 in standard form. Show your work. Justify each step.
3
Other
35. Explain why the equation 6 |x | + 22 = 4 has no solution.
4
ID: A
Algebra Unit 7 Review Packet
Answer Section
SHORT ANSWER
1. d ≤ − 8 or d ≥ 4
2. –17 < x < 8
3.
4.
5.
6.
7.
x = 13 or x = –13
n = 14 or n = –14
no solution
h = –7, h = 21
–2x + 3y = 21
2
8. y = x − 6
5
9.
10.
1
ID: A
3
(x − 4)
5
12. y + 9 = −2(x – 10)
5
13. y + 1 = (x – 2); –5x + 6y = –16
6
11. y + 6 =
5
14. The relationship is linear; y + 2 = − (x + 9).
4
15. The relationship is not linear.
16. y – 9 = 3(x –3); 36 cm
17. Yes, since the slope are the same and the y-intercepts are different.
18. No, since the slopes are different.
19. y = –5x – 27
3
20. y = x – 12
4
21. neither
22. perpendicular
23. y = −3x + 29
3
24. y = − x − 4
2
25. y = 4.9x + 17.1; about 56 words per minute
26.
27. y = | x | + 2
28. y = | x + 6 |
29. y = | x – 16.5 |
2
ID: A
30.
31.
32.
33. Answers may vary. Sample given:
y = 3x; 36 cards
3
ID: A
ESSAY
34.
[4]
5
x − 11
3
ÊÁ 5
ˆ˜
3y = 3 ÁÁÁÁ x − 11 ˜˜˜˜ Multiply each side by 3.
Ë3
¯
y =
3y = 5x − 33
−5x + 3y = −33
[3]
[2]
[1]
Use the Distributive Property.
Subtract 5x from each side.
correct steps with no justification OR one computational error
more than one computational error
more than one computational error and no justification
OTHER
35. 4 − 22 equals –18, and
−18
equals –3, which is also negative. Since |x | can never be negative, there is no
6
solution.
4