Graphing Linear Equations Chapter Questions
1. What are the various types of information you can be given to graph a line?
2. What is slope? How is it determined?
3. Why do we need to be careful about the slopes of horizontal and vertical lines?
4. How can we tell is two lines are parallel, perpendicular or neither just from their equations?
5. What are the various ways you can use information given to you to determine the equation of a line?
6. What are the different ways to solve a system of linear equations?
7. When do you get an answer to a system of linear equations that has one solution, no solution and
infinitely many solutions?
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Graphing Linear Equations Chapter Problems
Tables
Classwork
For the equations below, make a table with at least 3 ordered pairs, plot the points and connect them to
form the line.
1) y = 3x - 4
2) y = -2x + 4
3) y = x – 3
4) y = x + 4
5) y = - x + 1
Homework
For the equations below, make a table with at least 3 ordered pairs, plot the points and connect them to
form the line.
6) y = -x – 2
7) y = 2x + 1
8) y = x
9) y = -2x – 2
10) y = - x + 4
Slope and y-intercept
Classwork
11) Use lines A, B, C and D to fill in the table.
Lines
y intercept
Slope (+, -, 0 or
undefined
A
B
C
D
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12) What is the slope of lines E, F, G and H?
Lines
slope
E
F
G
H
13) What are the equations of lines E, F ,G and H?
Lines
Equation
E
F
G
H
Homework
14) Use lines I, J, K and L to fill in the table.
Lines
y intercept
Slope (+, -, 0 or
undefined
I
J
K
L
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15) What are the slopes of lines M, N, O and P?
Lines
slope
M
N
O
P
16) What is the equation of lines M, N, O and P?
Lines
Equation
M
N
O
P
Slope Formula
Classwork Find the slope of the line through each of the following two points.
17) (-12,-5), (0,-8)
18) (12,-18),(11,12)
19) (-18,-20),(-18,-15)
20) (-20,-4),(-12,-10)
21) (8,10),(0,14)
22) (6,9),(3,-9)
23) (1,2),(5,7)
24) (3,-3),(12,-2)
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25) (-4,-8),(-1,1)
26) (4,7),(-3,7)
Homework Find the slope of the line through each of the following two points.
27) (3,-9),(1,1)
28) (7,4),(3,8)
29) (-3,0),(5,12)
30) (8,-2),(12,-2)
31) (6,-3),(2,9)
32) (-3,7),(-4,8)
33) (5,9),(5,-8)
34) (-5, 0.5),(-6,3)
35) (-7,1),(7,8)
36) (-2,1),(5,7)
Slope Intercept Form
37) Write the equation for each graph that is for the line.
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Which graph represents the following equations?
38) y = - 4
39) y = -x + 5
40) y = -3/8x – 6
41) y = 3/2x
Homework
42) Write the equation that represents the following
graphs.
Which graph represents the following equations?
43) y = -4/5 -8
44) y = 8
45) y = 5/4x -1
46) y = -3x + 2
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Rate of Change
Classwork
47) If a car passes mile-marker 50 in 2 hours and mile-marker 200 in 6 hours, how many miles per
hour is the car traveling?
48) A driver sets the cruise controls at 55 miles per hour. After driving for 3 hours, he passes milemarker 650. In 2 hours, what mile-marker will he be passing?
49) Dominique earns $10 per hour for tutoring students and is given $15 for gas everyday. Write an
equation that represents the situation.
50) Maria spends $200.50 on groceries in a week but earned $4000 total at her last job. Write an
equation that represents the situation.
51) John has a company that charges $4/lb. for gourmet candy plus $7 shipping. If Lisa buys 6 lbs. of
candy, how much money will she spend?
Homework
52) If a car passes mile-marker 25 in 2 hours and mile-marker 450 in 5 hours, how many miles per
hour is the car traveling?
53) A driver sets the cruise controls at 45 miles per hour. After driving for 2 hours, he passes milemarker 20. In 3 hours, what mile-marker will he be passing?
54) Christina earns $7.50 per hour for tutoring students and is given $50 for gas everyday. Write an
equation that represents the situation.
55) Monique spends $400 on groceries in a week but earned $15,000 total at her last job. Write an
equation that represents the situation.
56) Timothy has a company that charges $9/lb. for gourmet candy plus $7 shipping. If Janice buys 3
lbs. of candy, how much money will she spend?
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Proportional Relationships and Graphing
Classwork
For each problem, draw the graph of the relationship between the two quantities & state what the slope is.
57) A maple tree grows 8 inches each year.
58) Coconuts are $4.50 per pound.
59) Every 5 days, Lilo receives 6 flowers from Stitch.
60) Barney makes 4 pies an hour.
61) Aladdin takes a carpet ride every 5 days.
62) Speed Racer drives a race every 3 years.
63) Brooke puts $5.00 in her bank account every week.
64) Peyton grades a quiz every 30 seconds.
Homework
65) A palm tree grows 2 inches each year.
66) Pineapples are $2.00 per pound.
67) Every 3 days, Lilo receives 4 flowers from Stitch.
68) Princess Fiona makes 8 puzzles in her tower in 3 hours.
69) Jasmine takes a carpet ride every 3 days.
70) Mach 5 drives a race every 7 days.
71) Hayley puts $20.00 in her bank account every week.
72) Lucas grades a test every 2 minutes and 30 seconds.
Slope & Similar Triangles
Classwork
Find the slope of the hypotenuse from the triangle with the following points.
73) (0,0); (0,4); (7,0)
74) (1,3); (1,7); (-4,3)
75) (-3,2); (-3,3); (-5,3)
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76) (1,1); (1,5); (2,5)
77) Find three points that form a triangle that lies on a line with a slope of 3/5.
78) State whether triangle A and triangle B are congruent, similar, or neither.
a. Triangle A: (1,5) (1,9) (3,9)
Triangle B: (-3,0) (-3,3) (-1,3)
b. Triangle A: (2,5) (2,7) (5,7)
Triangle B: (-2,2) (4,2) (4,6)
c. Triangle A: (3,4) (1,4) (8,12)
Triangle B: (1,-5) (-2,-6) (2,5)
79) Consider a slide. The top of the slide is 7 ft from the ground. The base of the slide is 10 ft from
the ladder. What is the slope of the slide? If you were at the base of the slide, and moved 2 feet
closer to the slide, how high is the slide at this point? How high off the ground would the slide be if
you moved the slide base 2 ft towards where the ladder was? How far from the ladder would the base
of the slide need to be placed if you wanted the slide to have a slope of 1/2?
Homework
Find the slope of the hypotenuse from the triangle with the following points.
80) (7,1); (4,0); (7,0)
81) (0,2); (0,6); (-5,2)
82) (-2,3); (-2,4); (-4,4)
83) (-2,-2); (-2,2); (-1,2)
84) Find three points that form a triangle that lies on a line with a slope of 2/5.
85) State whether triangle A and triangle B are congruent, similar, or neither.
a. Triangle A: (6,10) (6,14) (8,14)
Triangle B: (-1,2) (-1,5) (1,5)
b. Triangle A: (6,9) (6,11) (9,11)
Triangle B: (-6,-9) (-6,-11) (-9,-11)
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c. Triangle A: (3,6) (1,4) (1,12)
Triangle B: (1,-5) (1,-6) (5,5)
86) Consider a slide. The top of the slide is 4 ft from the ground. The base of the slide is 2.5 ft from
the ladder. What is the slope of the slide? How high off the ground would the slide be if you moved
the slide base .5 ft towards where the ladder was? How far from the ladder would the base of the
slide need to be placed if you wanted the slide to have a slope of 1/2?
Parallel and Perpendicular Lines
Classwork
87)
What is a line parallel to y = -4/5x + 7?
88)
What is a line parallel to y = -4x -4?
89)
What is a line parallel to y = x?
90)
What is a line parallel to y = 0?
91)
What is a line perpendicular to y = 1/2x + 5?
92)
What is a line perpendicular to y = -3/4x +4?
93)
What is a line perpendicular to y = x?
94)
What is a line perpendicular to y = -5x + 2?
Homework
95)
What is a line parallel to y = 3/8x + 4?
96)
What is a line parallel to y = -2x -7?
97)
What is a line parallel to y = 3x?
98)
What is a line parallel to y = 2?
99)
What is a line perpendicular to y = -1/2x + 1?
100) What is a line perpendicular to y = 3/7x -4?
101) What is a line perpendicular to y = 9x?
102) What is a line perpendicular to y = -11/2x - 16?
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Systems: Solve by graphing
Classwork
103)
y = -x – 7
4
y= x–7
3
104)
1
y=- x+2
4
1
y=- x+3
2
105)
y = -3x – 5
y=x+3
106)
y = -2x + 5
1
y= x–2
3
107)
y = -4x + 7
y = -3x + 3
108)
y= x–3
3
4
3
y= x+2
4
109)
4
y= x+3
3
2
y=- x–3
3
110)
1
y= x+2
3
y = -x – 2
111)
y = 4x – 1
y = -x + 4
112)
y = 3x – 4
y = 4x + 10
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Homework
113)
3
2
1
-2
y=- x–4
y=
+1
114)
y = -2x – 2
y = -3x – 6
115)
y=x–2
y=x+2
116)
y= x+1
3
4
1
y=- x–4
2
117)
y=x–4
y = -x + 2
118)
y = -4x – 1
y = x – 11
119)
y = -3x – 3
1
y= x+4
2
120)
2
y=- x+3
5
2
y= x–1
5
121)
y = -x – 2
1
y=- x+2
2
122)
y=x+5
y = -x + 3
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Systems: Solve by Substitution
Classwork
123)
x = 4y – 9
x=y+3
124)
5x = -2y + 48
x = -3y + 20
125)
y – 4x = 28
y = -2x – 2
126)
y + 2x = -12
y = x + 15
127)
x = -2y – 7
2x + y = -14
128)
x = 5y – 38
x = -4y + 16
129)
y = 2x + 3
4x – 2y = 8
130)
x = -4y + 8
x = 3y + 8
131)
5y + 5x = 85
y = 4x – 18
132)
x = y – 12
x = 5y – 40
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Homework
133)
y = -5x + 41
-2x = -14 – 2y
134)
y = 3x + 6
-6x + 2y = 12
135)
y – 3x = 0
y = -3x – 18
136)
x = -3y + 13
4x – 4y = 20
137)
x = -4y + 29
5x + 2y = 37
138)
y = -2x + 11
5y – 2x = 31
139)
5y – 5x = -15
y = -3x + 29
140)
-4x = 3y + 32
x = -5y – 8
141)
y = -3x – 1
-4y + x = -9
142)
y = -4x + 17
-3y – x = -7
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Systems: Solve by Elimination (Addition & Subtraction)
Classwork
143)
3x + y = 36
5x + y = 56
144)
x + 2y = 25
x + 3y = 33
145)
3x – 5y = -52
x – 5y = -34
146)
2x + 3y = 4
-2x + 5y = 60
147)
2x + 2y = 2
5x – 2y = 40
148)
-x + 2y = 14
x – 2y = -11
149)
4x – y = 16
4x + 2y = 16
150)
2x + 5y = 5
-2x + y = -23
151)
2x – 2y = -12
x – 2y = -13
152)
5x + 5y = 40
-5x + 3y = -40
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Homework
153)
4x – y = -2
4x + 5y = 10
154)
2x + 4y = 10
-4x + 4y = 52
155)
-3x – 5y = 49
3x + 4y = -44
156)
-4x + 3y = 39
5x – 3y = -45
157)
-5x – 2y = -5
-x – 2y = -1
158)
x + 5y = -4
-x + 2y = -10
159)
-4x + 2y = -44
4x + 4y = 20
160)
x + 2y = 4
x + 5y = -2
161)
3x – y = -5
-3x – 2y = -10
162)
3x – y = 11
-3x – 5y = -71
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Systems: Solve by Elimination (Multiply First)
Classwork
163)
5x – 4y = 47
-x – 16y = 125
164)
3x – 2y = 33
-4x – 4y = 16
165)
2x + y = 21
4x + 3y = 51
166)
-3x + 3y = -27
12x + 5y = 108
167)
3x + 4y = 3
-12x – y = -57
168)
2x + 5y = -7
8x + 3y = 57
169)
4x + 3y = 33
8x + y = 31
170)
3x – 2y = 11
4x – 8y = 36
171)
–x – y = -8
-4x + 2y = 22
172)
2x + y = 0
-8x + 4y = 80
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Homework
173)
–x + y = -5
-3x + 4y = -12
174)
-2x – y = 2
-6x + 3y = -18
175)
-2x + 2y = 16
6x – y = -13
176)
-4x – 5y = -9
3x + 10y = 13
177)
3x – 2y = -26
6x – 4y = -70
178)
x + 5y = -12
3x + y = 6
179)
x + y = 14
4x – 2y = 2
180)
-3x + 3y = -3
-12x + 5y = -61
181)
3x + 2y = 27
-9x + 4y = -51
182)
4x + 4y = 20
2x – 16y = -44
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Systems: Choose Your Own Strategy
Classwork
183)
–x + 4y = 5
x + 4y = 11
184)
3x – y = 7
4x – 2y = 8
185)
2y + 5x = 35
y = 4x – 28
186)
5x – 4y = -39
-3x – 4y = -15
187)
y = -5x + 59
4x + y = 49
188)
y=x+6
4
y= x+6
5
189)
-2x + 4y = 28
2x – 3y = -18
190)
y = -x + 12
3y + 3x = 36
191)
2x + 4y = -10
-4x – 12y = 36
192)
–x – 5y = -3
-2x + 5y = 9
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Systems: Choose Your Own Strategy
Homework
193)
-3x + 5y = -39
12x – 4y = 60
194)
y = 3x – 18
y – 3x = -24
195)
x + 3y = 16
-x + 4y = 5
196)
x = -3y – 19
x + 5y = -22
197)
3x – 3y = 12
9x + 2y = 102
198)
y=- x+4
4
3
2
y = x + 10
3
199)
3x + 2y = 21
-3x + 5y = 21
200)
–x – y = 7
-x + 5y = 19
201)
4x + y = -28
-2x + 2y = 24
202)
x = 2y – 7
-x + 4y = 17
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Writing Systems to Model Situations
Classwork
203)
The admission fee at a carnival is $3.00 for children and $5.00 for adults. On the first day
1,500 people enter the fair and $5740 is collected. How many children and how many adults attended
the carnival?
204)
A builder placed two orders with the hardware store. The first order was for 25 sheets of
plywood and 4 boxes of nails and the bill totaled $357. The second order was for 35 sheets of
plywood and 2 boxes of nails and the bill totaled $471. The bills do not list the per-item price. What
were the prices of one piece of plywood and one box of nails?
Homework
205)
Two friends bought some markers and pens. The first bought 4 markers and 5 pens and
it cost him $6.71. The second friend bought 5 markers and 3 pens, which cost her $7.12. What is the
price for one marker and one pen?
206)
The ticket price for the movies is $7.50 for children and $10.50 for adults. One night 825
people bought tickets and $8005.50 was collected from ticket sales. How many children and how
many adults bought tickets.
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Answer Key
Tables
Homework
Classwork
1-5 Answers will vary
14)
Homework
6-10 Answers will vary
Slope and y-intercept
Classwork
11)
Lines
A
B
C
D
Lines
y intercept
Slope (+, -, 0 or
undefined
I
J
K
L
8
3
-1
-8
0
+
+
15)
y intercept
Slope (+, -, 0 or
undefined
0
6
-5
-2
+
+
0
Lines
Equation
M
N
O
P
-1
2
0
-1/3
Lines
Equation
M
N
O
P
y = -x+5
y = 2x
y = -4
y = -1/3x - 6
16)
12)
Lines
slope
E
F
G
H
½
-2
Undefined
1
13)
Lines
Equation
E
F
G
H
y = 1/2x + 1
y = -2x + 4
x=8
y=x-7
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Slope Formula
Classwork
17) -1/4
18) -30
19) undefined
20) -3/4
21) -1/2
22) 6
23) 5/4
24) 1/9
25) 3
26) 0
Homework
27) -5
28) -1
29) 3/2
30) 0
31) -3
32) -1
33) undefined
34) -2.5
35) ½
36) 6/7
Slope Intercept Form
Classwork
37a) y = -2x+1
37b) y = -1/2x
37c) y = -x+1
37d) y = -2/5x – 1
37e) y = -3/2x – 3
38) line O
39) line M
40) line P
41) line N
Homework
42a) y = 3/2x – 2
42b) y = x + 1
42c) y = 2x – 3
42d) y = 1/2x + 3
42e) y = x
42f) y = 2x
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Rate of Change
Classwork
47) 37.5 mph
48) mile marker 760
49) y = 10x + 15, x being number of hours
50) y = -200.50x + 4000, x being number of weeks
51) $31
Homework
52) 141.7 mph
53) mile marker 155
54) y = 7.50x + 50, x being number of hours
55) y = -400x + 15,000, x being number of weeks
56) $34
Proportional Relationships and Graphing
Classwork
57) y = 8x
58) y = 4.50x
59) y = 6/5x
60) y = 4x
61) y = 1/5x
62) y = 1/3x
63) y = 5x
64) y = 1/30x
Homework
65) y = 2x
66) y = 2x
67) y = 4/3x
68) y = 8/3x
69) y = 1/3x
70) y = 1/7x
71) y = 20x
72) y = 2/5x
Slopes & Similar Triangles
Classwork
73) -4/7
74) 4/5
75) -1/2
76) 4
77) answers will vary
78a) neither
78b) similar
78c) neither
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43) line L
44) line I
45) line K
46) line J
Homework
80) 1/3
81) 4/5
82) -1/2
83) 4
84) answers will vary
79) The slope of the slide is 7/10. The slide would
be 1.4 ft high. The base of the slide would need to
be 14 feet away if you wanted a slope of ½.
104) (4,1)
85a) neither
85b) congruent
85c) neither
86) Slope of the slide is 8/5. The slide would be .8
ft high. The base of the slide would need to be 8
feet away.
Parallel and Perpendicular Lines
Classwork
87 – 94 Answers will vary
Homework
95-102 Answers will vary
105) (-2,1)
Systems: Solve by Graphing
Classwork
103) (0,-7)
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106) (3,-1)
109) (-3, -1)
107) (4, -9)
110) (-3, 1)
108) no solution
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111) (1, 3)
114) (-4,6)
112) (-14, -46)
115) no solution
Homework
113) (-5, 3.5)
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116) (-4, -2)
118) (2, -9)
119) (-2, 3)
117) (3, -1)
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120) (5, 1)
122) (-1, 4)
121) ( -8, 6)
Systems: Solve by Substitution
Classwork
123) (7, 4)
124) (8,4)
125) (-5, 8)
126) (-9, 6)
127) (-7, 0)
128) (-8, 6)
129) no solution
130) (8, 0)
131) (7, 10)
132) (-5, 7)
Homework
133) (8,1)
134) ∞ solutions
135) (-3, -9)
136) (7, 2)
137) (5, 6)
138) (2, 7)
139) (8, 5)
140) (-8, 0)
141) (-1, 2)
142) (4, 1)
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Systems: Solve by Elimination (Add & Subtract)
Classwork
143) (10, 6)
144) (9, 8)
145) (-9, 5)
146) (-10, 8)
147) (6, -5)
148) no solution
149) (4, 0)
150) (10, -3)
151) (1, 7)
152) (8, 0)
Homework
153) (0, 2)
154) (-7, 6)
155) (-8, -5)
156) (-6, 5)
157) (1, 0)
158) (6, -2)
159) (9, -4)
160) (8, -2)
161) (0, 5)
162) (7, 10)
Systems: Solve by Elimination (Multiply First)
Classwork
163) (3, -8)
164) (5, -9)
165) (6, 9)
166) (9, 0)
167) (5, -3)
168) (9, -5)
169) (3, 7)
170) (1,4)
171) (-1, 9)
172) (-5, 10)
NJ Center for Teaching and Learning
Homework
173) (8,3)
174) (1, -4)
175) (-1, 7)
176) (1, 1)
177) no solution
178) (3, -3)
179) (5, 9)
180) (8, 7)
181) (7, 3)
182) (2, 3)
Systems: Choose Your Own Strategy
Classwork
183) (3, 2)
184) (3, 2)
185) (7, 0)
186) (-3, 6)
187) (10, 9)
188) (0, 6)
189) (6, 10)
190) ∞ solutions
191) (3, -4)
192) (-2, 1)
Homework
193) (3, -6)
194) no solution
195) (7, 3)
196) (-29/2, -3/2)
197) (10, 6)
198) (-3, 8)
199) (3, 6)
200) (-9, 2)
201) (-8, 4)
202) (3, 5)
Writing Systems to Model Situations
Classwork
203) 620 adults, 880 children
204) $13 for plywood, $8 for box of nails
Homework
205) marker costs $1.19, pen costs $0.39
206) 219 children, 606 adults
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Graphing Linear Equations
Unit Review
PMI - Eighth Grade
Name:_________________
Date: _________________
Multiple choice questions: choose the correct answer.
1. What is the y-intercept of a line?
a. The point at which the line crosses the origin.
b. The point at which the line crosses the y-axis.
c. The point at which the line crosses the x-axis.
d. The point at which the line stops
2. All of the following statements about the slope of a line are true except:
a. Slope is rise over run of a line.
c. Slope can be negative.
b. Slope is run over rise.
d. Slope can be undefined.
3.
For the slope intercept form, y = mx+b, the m is:
a. Slope
b. y-intercept
c. x-intercept
d. line
4. For the slope intercept form, y = mx+b, the b is:
a. Slope
b. y-intercept
c. x-intercept
d. line
5. The slope is _____ for the line x = -5.
a. Positive
b. Negative
c. Zero
d. Undefined
6. The slope is _____ for the line y=x.
a. Positive
b. Negative
c. Zero
d. Undefined
7. The slope is _____ for the line y =-x.
a. Positive
b. Negative
c. Zero
d. Undefined
8. Given a line with the equation y = -2/3x+5, what would be the slope of the line that is perpendicular to
this line?
a. -2/3
c. -3
b. 2
d. 3/2
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9. Given a line with the equation y =-9x+12, what would be the slope of the line that is perpendicular to
this line?
a. -9
c. -1/9
b. 1/9
d. 9
10. The line that passes through the points (2, 2) and (2, -2) has a slope that is:
a. Positive
c. Zero
b. Negative
d. Undefined
11. The line that passes through the points (-10, 2) and (12, 6) has a slope that is:
a. Positive
c. Zero
b. Negative
d. Undefined
12. What is the slope of the line that passes through the points (8,-2) and (12, -2)?
a. -5
c. Zero
b. ½
d. Undefined
13. What is the slope of the line that passes through the points (-3,0) and (5, 12)?
a. 3
c. -3/2
b. ½
d. 3/2
14. What is the slope of the line that passes through the points (-7,1) and (7,8)?
a. ½
c. -1/2
b. 2
d. -2
15. The following points lie on the line y =2x + 7, except:
a. (1, 9)
b. (-2, 3)
c. (4, 12)
d. (-4, 1)
16. The following points lie on the line y = -2/3x-4, except:
a. (0, -4)
b. (-3, -2)
c. (-6, 9)
d. (-12, 4)
17. If Sarah can make $30 a week babysitting, and she deposits her money into a savings account that
originally had $100 dollars, how much will she have after 5 weeks?
a. $150
c. $200
b. $100
d. $250
18. If you were to write an equation for the amount of money Sarah has from question 16, what would be
the y-intercept?
a. $150
c. $200
b. $100
d. $250
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19. A car traveling a constant speed of 55 miles an hour passed mile marker 126 on the interstate. After 3
hours of traveling, what mile marker will it have passed?
a. Mile marker 391
c. Mile Marker 291
b. Mile marker 290
d. Mile Marker 165
20. Monique earned $15,000 for her contract job. She spends $250 a week on living expenses. After 6
weeks, how much will she have left?
a. $13,000
c. $12,000
b. $13,500
d. $11,400
21. What is true about the lines y = -x-7 and y = 4/3x-7?
a. They have the same y-intercept.
b. They are parallel.
c. They are perpendicular.
d. They have the same slope.
22. What is true about the lines y = x+2 and y = -x-2?
a. They have the same y-intercept.
b. They are parallel.
c. They are perpendicular.
d. They have the same slope.
23. John raised his candy price to $6 per lb. He also raised shipping prices to $10 per order. Kathy ordered
6 lbs. of candy on Monday, but then she realized she needed more. She placed a separate order of 2
lbs. on Tuesday. How much did she spend on both orders?
a. $58.00
c. $70.00
b. $68.00
d. $78.00
24. Payal made $400 from her last job. Each week, she spends $20 on food. Which equation would
represent how much money she has left after x number of weeks?
a. y =20x+400
c. y =-20x+400
b. y = 20x-400
d. y =-20x-400
25. Suppose Payal had $600 just prior to her last job. Using the information from question 23, which
equation will represent how much money she has after x number of weeks?
a. y =20x+1000
c. y =-20x+1000
b. y = 20x-600
d. y =-20x-600
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Short Constructed Response Questions: Solve each problem, and write the answer on the line.
For questions 26-35 refer to the following graph.
State if the slope is +, -, 0, or undefined for the
following:
26. Line A: _____
27. Line B: _____
28. Line C: _____
29. Line D: _____
30. Line E: _____
Write the equation for the following lines:
31. Line A:____________________
32. Line B:____________________
33. Line C:____________________
34. Line D:____________________
35. Line E:____________________
Solve the following systems of equations:
36. x = 4y-0, x = y+3
37. y =2x+3, 4x-27 = 8
38. y = 10x+20, -30x + 3y = 60
39. –x-y=-8, -4x+2y = 22
40. y = 3x-18, y-3x+ -24
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Answer: ____________________
Answer: ____________________
Answer: ___________________
Answer:____________________
Answer: ____________________
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Extended Constructed Response Questions:
41. Consider a slide shaped like a right triangle. The base of the slide is 20 feet away from the ladder. The
top of the slide is 8 feet high. Hint: Draw a picture
a. What is the slope of the slide?
b. Write an equation for the line that the slide would form.
c. Let’s say you were standing at the bottom of the slide, and walked 5 feet closer to the ladder.
How high is the slide at this point?
d. If the slide was 22 feet long, what would be the new slope?
42. Bob sells pineapples in a pineapple stand in Lahaina, Hawaii. Today, he has 100 pineapples to sell.
Based on his experience, he usually sells about 10 pineapples per hour.
a. Write an equation that represents how many pineapples he can sell in one day.
b. Using your equation from part a, draw a graph.
c. If he starts selling at 10 a.m., how many pineapples has he sold so far at 2 p.m.?
d. What time will he have sold all of his pineapples?
43. Fred placed an order with the furniture store. He ordered metal chairs at $25 each and plastic chairs at
$10 each. His order totaled $450.00. There were 30 chairs he ordered. How many of each chair did he
order?
a. Write a system of equations that describes this situation, and define your variables.
b. How many of each chair did he order?
44. A group of 148 people is spending five days at a summer camp. The cook ordered 12 pounds of food
for each adult and 9 pounds of food for each child. A total of 1,410 pounds of food was ordered.
a. Write a system of equations that describes this situation, and define your variables.
b. Solving the system of equations from part a, find the number of adults and number of children
that were at the camp.
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Graphing Linear Equations –Unit Review
Answer Key
1. B
21. A
2. B
22. C
3. A
23. B
4. B
24. C
5. D
25. C
6. A
26. Undefined
7. B
27. 0
8. D
28. Negative
9. B
29. Positive
10. D
30. Negative
11. A
31. x = -7
12. C
32. y = -5
13. D
33. y = -5/2x
14. A
34. y = x
15. D
35. y = - 1/4x+8
16. C
36. (4,1)
17. D
37. No solution
18. B
38. infinitely many solutions
19. C
39. (-1,9)
20. B
40. No solution
41. A. depending on the way the student drew the slide, the slope should be 2/5 or -2/5 B. y=2/5x+8 C. 2 ft
off the ground. D. 4/11
42. A. y = -10x + 100 C. 40 pineapples D. 8 p.m.
43. A. m = number of metal chairs, p = number of platic chairs, m + p= 30, 25m + 10p = 400 B. Fred
ordered 10 metal chairs and 20 plastic chairs.
44. A. a = number of adults, c = number of children, a + c =148, 12a + 9c=1,410. B. 26 adults, 122 children
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