Download Algebra 1 - Chapter 6 Review

Algebra 1 - Chapter 6 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Match the equation with its graph.
____
1. –7x + 7y = –49
a.
–10 –8
–6
–4
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
10
–4
–6
–4
–2
–2
–4
–6
–6
–8
–8
–10
–10
y
–6
–10 –8
x
–4
b.
–10 –8
y
c.
y
10
8
8
6
6
4
4
2
2
2
4
6
8
10
x
4
6
8
10
x
2
4
6
8
10
x
y
d.
10
–2
–2
2
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
Short Answer
The rate of change is constant in each table. Find the rate of change. Explain what the rate of change
means for the situation.
2.
Time (days)
Cost ($)
3
75
4
100
5
125
6
150
The rate of change is constant in the graph. Find the rate of change. Explain what the rate of change
means for the situation.
3.
Resale Value of a Refrigerator
600
Amounts ($)
500
400
300
200
100
3
6
9
12
15
18
Years after original purchase
Find the rate of change for the situation.
4. You run 7 miles in one hour and 21 miles in three hours.
Find the slope of the line.
y
5.
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
Find the slope of the line that passes through the pair of points.
6. (1, 7), (10, 1)
7. A student finds the slope of the line between (14, 1) and (18, 17). She writes
make?
. What mistake did she
Find the slope and y-intercept of the line.
8.
y=
4
x–3
3
Write an equation of a line with the given slope and y-intercept.
9. m = 1, b = 4
10. Use the slope and y-intercept to graph the equation.
3
y= x–3
4
Find the x- and y-intercept of the line.
11. 2x + 3y = –18
12. Write y =
2
x + 7 in standard form using integers.
3
13. Write an equation of a line that has the same slope as 2x – 5y = 12 and the same y-intercept as 4y + 24 = 5x.
Graph the equation.
14. y + 2 = –(x – 4)
Write an equation in point-slope form for the line through the given point with the given slope.
15. (4, –6); m =
16. 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.
Is the relationship shown by the data linear? If so, model the data with an equation.
17.
x
y
–9
–2
–5
–7
–1
–12
–17
3
18. 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
Are the graphs of the lines in the pair parallel? Explain.
1
x+8
6
–2x + 12y = –11
19. y =
Write an equation for the line that is parallel to the given line and that passes through the given point.
20. y = –5x + 3; (–6, 3)
21. y =
3
x – 9; (–8, –18)
4
Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
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.
23.
; (–6, 5)
Algebra 1 - Chapter 6 Review
Answer Section
MULTIPLE CHOICE
1. ANS:
OBJ:
NAT:
TOP:
KEY:
A
PTS: 1
DIF: L2
REF: 6-4 Standard Form
6-4.1 Graphing Equations Using Intercepts
NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2
STA: TX TEKS A.1C | TX TEKS A.6E
6-4 Example 2
graphing | x-intercept | y-intercept | standard form of a linear equation
SHORT ANSWER
2. ANS:
dollars per day; the cost is $25 for each day.
PTS:
OBJ:
NAT:
STA:
KEY:
3. ANS:
1
DIF: L2
REF: 6-1 Rate of Change and Slope
6-1.1 Finding Rates of Change
NAEP 2005 M1 | NAEP 2005 A2a | NAEP 2005 A2b | ADP J.4.1 | ADP K.10.1
TX TEKS A.6A | TX TEKS A.6B TOP: 6-1 Example 1
rate of change
; value drops $100 every 3 years.
PTS: 1
DIF: L2
REF: 6-1 Rate of Change and Slope
OBJ: 6-1.1 Finding Rates of Change
NAT: NAEP 2005 M1 | NAEP 2005 A2a | NAEP 2005 A2b | ADP J.4.1 | ADP K.10.1
STA: TX TEKS A.6A | TX TEKS A.6B TOP: 6-1 Example 2
KEY: graphing | rate of change
4. ANS:
7 miles per hour
PTS:
OBJ:
NAT:
STA:
5. ANS:
1
3
1
DIF: L3
REF: 6-1 Rate of Change and Slope
6-1.1 Finding Rates of Change
NAEP 2005 M1 | NAEP 2005 A2a | NAEP 2005 A2b | ADP J.4.1 | ADP K.10.1
TX TEKS A.6A | TX TEKS A.6B KEY: rate of change
PTS:
OBJ:
NAT:
STA:
KEY:
6. ANS:
1
DIF: L2
REF: 6-1 Rate of Change and Slope
6-1.2 Finding Slope
NAEP 2005 M1 | NAEP 2005 A2a | NAEP 2005 A2b | ADP J.4.1 | ADP K.10.1
TX TEKS A.6A | TX TEKS A.6B TOP: 6-1 Example 3
finding slope using a graph | slope | graphing

2
3
PTS: 1
DIF: L2
REF: 6-1 Rate of Change and Slope
OBJ: 6-1.2 Finding Slope
NAT: NAEP 2005 M1 | NAEP 2005 A2a | NAEP 2005 A2b | ADP J.4.1 | ADP K.10.1
STA: TX TEKS A.6A | TX TEKS A.6B TOP: 6-1 Example 4
KEY: finding slope using points | slope
7. ANS:
She did not keep the order of the points the same in numerator and the denominator.
PTS:
OBJ:
NAT:
STA:
KEY:
8. ANS:
4
; –3
3
1
DIF: L3
REF: 6-1 Rate of Change and Slope
6-1.2 Finding Slope
NAEP 2005 M1 | NAEP 2005 A2a | NAEP 2005 A2b | ADP J.4.1 | ADP K.10.1
TX TEKS A.6A | TX TEKS A.6B TOP: 6-1 Example 4
slope | reasoning | error analysis
PTS: 1
DIF: L2
REF: 6-2 Slope-Intercept Form
OBJ: 6-2.1 Writing Linear Equations
NAT: NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2
STA: TX TEKS A.2A | TX TEKS A.4C | TX TEKS A.6A | TX TEKS A.6D | TX TEKS A.6E | TX TEKS
A.6G TOP:
6-2 Example 1
KEY: linear equation | y-intercept | slope
9. ANS:
y=x+4
PTS:
OBJ:
STA:
A.6G
10. ANS:
1
DIF: L2
REF: 6-2 Slope-Intercept Form
6-2.1 Writing Linear Equations
NAT: NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2
TX TEKS A.2A | TX TEKS A.4C | TX TEKS A.6A | TX TEKS A.6D | TX TEKS A.6E | TX TEKS
TOP:
6-2 Example 2
KEY: linear equation | slope | y-intercept
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
PTS: 1
DIF: L2
REF: 6-2 Slope-Intercept Form
OBJ: 6-2.2 Graphing Linear Equations
NAT: NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2
STA: TX TEKS A.2A | TX TEKS A.4C | TX TEKS A.6A | TX TEKS A.6D | TX TEKS A.6E | TX TEKS
A.6G TOP:
6-2 Example 4
11. ANS:
x-intercept is –9; y-intercept is –6.
KEY: linear equation | graphing equations | slope | y-intercept
PTS: 1
DIF: L2
REF: 6-4 Standard Form
OBJ: 6-4.1 Graphing Equations Using Intercepts
NAT: NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2
STA: TX TEKS A.1C | TX TEKS A.6E
TOP: 6-4 Example 1
KEY: standard form of a linear equation | x-intercept | y-intercept
12. ANS:
–2x + 3y = 21
PTS:
OBJ:
NAT:
TOP:
KEY:
13. ANS:
1
DIF: L2
REF: 6-4 Standard Form
6-4.2 Writing Equations in Standard Form
NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2
STA: TX TEKS A.1C | TX TEKS A.6E
6-4 Example 4
standard form of a linear equation | transforming equations
PTS:
OBJ:
NAT:
KEY:
14. ANS:
1
DIF: L4
REF: 6-4 Standard Form
6-4.2 Writing Equations in Standard Form
NAEP 2005 A1h | ADP J.4.1 | ADP J.4.2 | ADP K.10.2
STA: TX TEKS A.1C | TX TEKS A.6E
standard form of a linear equation
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
PTS: 1
DIF: L2
REF: 6-5 Point-Slope Form and Writing Linear Equations
OBJ: 6-5.1 Using Point-Slope Form
NAT: NAEP 2005 A1h | NAEP 2005 A1i | NAEP 2005 A2a | NAEP 2005 A2b | NAEP 2005 A3a | ADP
J.4.1 | ADP J.4.2 | ADP K.10.1 | ADP K.10.2
STA: TX TEKS A.5A | TX TEKS A.6A | TX TEKS A.6B | TX TEKS A.6D
TOP: 6-5 Example 1
KEY: point-slope form | graphing | linear equation
15. ANS:
PTS: 1
DIF: L2
REF: 6-5 Point-Slope Form and Writing Linear Equations
OBJ: 6-5.1 Using Point-Slope Form
NAT: NAEP 2005 A1h | NAEP 2005 A1i | NAEP 2005 A2a | NAEP 2005 A2b | NAEP 2005 A3a | ADP
J.4.1 | ADP J.4.2 | ADP K.10.1 | ADP K.10.2
STA: TX TEKS A.5A | TX TEKS A.6A | TX TEKS A.6B | TX TEKS A.6D
TOP: 6-5 Example 2
KEY: slope-intercept form | linear equation
16. ANS:
5
y + 1 = (x – 2); –5x + 6y = –16
6
PTS: 1
DIF: L3
REF: 6-5 Point-Slope Form and Writing Linear Equations
OBJ: 6-5.1 Using Point-Slope Form
NAT: NAEP 2005 A1h | NAEP 2005 A1i | NAEP 2005 A2a | NAEP 2005 A2b | NAEP 2005 A3a | ADP
J.4.1 | ADP J.4.2 | ADP K.10.1 | ADP K.10.2
STA: TX TEKS A.5A | TX TEKS A.6A | TX TEKS A.6B | TX TEKS A.6D
TOP: 6-5 Example 3
KEY: point-slope form | transforming equations | standard form of a linear equation | multi-part question
17. ANS:
5
The relationship is linear; y + 2 =  (x + 9).
4
PTS: 1
DIF: L2
REF: 6-5 Point-Slope Form and Writing Linear Equations
OBJ: 6-5.2 Writing Linear Equations Using a Table
NAT: NAEP 2005 A1h | NAEP 2005 A1i | NAEP 2005 A2a | NAEP 2005 A2b | NAEP 2005 A3a | ADP
J.4.1 | ADP J.4.2 | ADP K.10.1 | ADP K.10.2
STA: TX TEKS A.5A | TX TEKS A.6A | TX TEKS A.6B | TX TEKS A.6D
TOP: 6-5 Example 4
KEY: linear equation | linear data
18. ANS:
y – 9 = 3(x –3); 36 cm
PTS: 1
DIF: L3
REF: 6-5 Point-Slope Form and Writing Linear Equations
OBJ: 6-5.2 Writing Linear Equations Using a Table
NAT: NAEP 2005 A1h | NAEP 2005 A1i | NAEP 2005 A2a | NAEP 2005 A2b | NAEP 2005 A3a | ADP
J.4.1 | ADP J.4.2 | ADP K.10.1 | ADP K.10.2
STA: TX TEKS A.5A | TX TEKS A.6A | TX TEKS A.6B | TX TEKS A.6D
TOP: 6-5 Example 5
KEY: point-slope form | linear data | problem solving | word problem | multi-part question
19. ANS:
Yes, since the slope are the same and the y-intercepts are different.
PTS: 1
DIF: L2
REF: 6-6 Parallel and Perpendicular Lines
OBJ: 6-6.1 Parallel Lines
NAT: NAEP 2005 G3g | NAEP 2005 A2e | ADP K.2.1 | ADP K.2.2 | ADP K.10.1 | ADP K.10.2
STA: TX TEKS A.6A | TX TEKS A.6D TOP: 6-6 Example 1
KEY: parallel lines | slope
20. ANS:
y = –5x – 27
PTS: 1
DIF: L2
REF: 6-6 Parallel and Perpendicular Lines
OBJ: 6-6.1 Parallel Lines
NAT: NAEP 2005 G3g | NAEP 2005 A2e | ADP K.2.1 | ADP K.2.2 | ADP K.10.1 | ADP K.10.2
STA: TX TEKS A.6A | TX TEKS A.6D TOP: 6-6 Example 2
KEY: parallel lines | linear equation
21. ANS:
3
y = x – 12
4
PTS: 1
DIF: L2
REF: 6-6 Parallel and Perpendicular Lines
OBJ: 6-6.1 Parallel Lines
NAT: NAEP 2005 G3g | NAEP 2005 A2e | ADP K.2.1 | ADP K.2.2 | ADP K.10.1 | ADP K.10.2
STA: TX TEKS A.6A | TX TEKS A.6D TOP: 6-6 Example 2
KEY: parallel lines | linear equation
22. ANS:
perpendicular
PTS:
OBJ:
NAT:
STA:
KEY:
23. ANS:
1
DIF: L3
REF: 6-6 Parallel and Perpendicular Lines
6-6.2 Perpendicular Lines
NAEP 2005 G3g | NAEP 2005 A2e | ADP K.2.1 | ADP K.2.2 | ADP K.10.1 | ADP K.10.2
TX TEKS A.6A | TX TEKS A.6D TOP: 6-6 Example 3
perpendicular lines | parallel lines
PTS:
OBJ:
NAT:
STA:
KEY:
1
DIF: L2
REF: 6-6 Parallel and Perpendicular Lines
6-6.2 Perpendicular Lines
NAEP 2005 G3g | NAEP 2005 A2e | ADP K.2.1 | ADP K.2.2 | ADP K.10.1 | ADP K.10.2
TX TEKS A.6A | TX TEKS A.6D TOP: 6-6 Example 3
perpendicular lines | linear equation