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?
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 undefinedA
B
C
D
12) What is the slope of lines E, F, G and H?
Lines / slopeE
F
G
H
13) What are the equations of lines E, F ,G and H?
Lines / EquationE
F
G
H
Homework
14) Use lines I, J, K and L to fill in the table.
Lines / y intercept / Slope (+, -, 0 or undefinedI
J
K
L
15) What are the slopes of lines M, N, O and P?
Lines / slopeM
N
O
P
16) What is the equation of lines M, N, O and P?
17)
Lines / EquationM
N
O
P
Slope Formula
Classwork Find the slope of the line through each of the following two points.
18) (-12,-5), (0,-8)
19) (12,-18),(11,12)
20) (-18,-20),(-18,-15)
21) (-20,-4),(-12,-10)
22) (8,10),(0,14)
23) (6,9),(3,-9)
24) (1,2),(5,7)
25) (3,-3),(12,-2)
26) (-4,-8),(-1,1)
27) (4,7),(-3,7)
Slope Formula
Homework Find the slope of the line through each of the following two points.
28) (3,-9),(1,1)
29) (7,4),(3,8)
30) (-3,0),(5,12)
31) (8,-2),(12,-2)
32) (6,-3),(2,9)
33) (-3,7),(-4,8)
34) (5,9),(5,-8)
35) (-5, 0.5),(-6,3)
36) (-7,1),(7,8)
37) (-2,1),(5,7)
Slope Intercept Form Classwork
38) Write the equation for each graph that is for the line.
Which graph represents the following equations?
39) y = - 4
40) y = -x + 5
41) y = -3/8x – 6
42) y = 3/2x
Slope Intercept Form Homework
43) Write the equation that represents the following graphs.
Which graph represents the following equations?
44) y = -4/5 -8
45) y = 8
46) y = 5/4x -1
47) y = -3x + 2
Rate of Change
Classwork
48) 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?
49) A driver sets the cruise controls at 55 miles per hour. After driving for 3 hours, he passes mile-marker 650. In 2 hours, what mile-marker will he be passing?
50) Dominique earns $10 per hour for tutoring students and is given $15 for gas everyday. Write an equation that represents the situation.
51) Maria spends $200.50 on groceries in a week but earned $4000 total at her last job. Write an equation that represents the situation.
52) 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
53) 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?
54) A driver sets the cruise controls at 45 miles per hour. After driving for 2 hours, he passes mile-marker 20. In 3 hours, what mile-marker will he be passing?
55) Christina earns $7.50 per hour for tutoring students and is given $50 for gas everyday. Write an equation that represents the situation.
56) Monique spends $400 on groceries in a week but earned $15,000 total at her last job. Write an equation that represents the situation.
57) 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?
Proportional Relationships and Graphing
Classwork
For each problem, draw the graph of the relationship between the two quantities & state what the slope is.
58) A maple tree grows 8 inches each year.
59) Coconuts are $4.50 per pound.
60) Every 5 days, Lilo receives 6 flowers from Stitch.
61) Barney makes 4 pies and hour.
62) Aladdin takes a carpet ride every 5 days.
63) Speed Racer drives a race every 3 years.
64) Brooke puts $5.00 in her bank account every week.
65) Peyton grades a quiz every 30 seconds.
Homework
66) A palm tree grows 2 inches each year.
67) Pineapples are $2.00 per pound.
68) Every 3 days, Lilo receives 4 flowers from Stitch.
69) Princess Fionna makes 8 puzzles in her tower in an 3 hours.
70) Jasmin takes a carper ride every 3 days.
71) Mock 5 drives a race every 7 days.
72) Hayley puts $20.00 in her bank account every week.
73) 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.
74) (0,0); (4,0); (7,0)
75) (1,3); (1,7); (-4,3)
76) (-3,2); (-3,3); (-5,3)
77) (1,1); (1,5); (2,5)
78) Find three points that form a triangle that lies on a line with a slope of 3/5.
79) 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) (-2,2) (4,6)
c. Triangle A: (3,4) (1,4) (8,12) Triangle B: (1,-5) (-2,-6) (2,5)
1
80) 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?
Slope & Similar Triangles
Homework
Find the slope of the hypotenuse from the triangle with the following points.
81) (1,1); (6,0); (7,0)
82) (0,2); (0,6); (-5,2)
83) (-2,3); (-2,4); (-4,4)
84) (-2,-2); (-2,2); (-1,2)
85) Find three points that form a triangle that lies on a line with a slope of 2/5.
86) 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)
c. Triangle A: (3,6) (1,4) (1,12) Triangle B: (1,-5) (1,-6) (5,5)
87) 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
88) What is a line parallel to y = -4/5x + 7?
89) What is a line parallel to y = -4x -4?
90) What is a line parallel to y = x?
91) What is a line parallel to y = 0?
92) What is a line perpendicular to y = 1/2x + 5?
93) What is a line perpendicular to y = -3/4x +4?
94) What is a line perpendicular to y = x?
95) What is a line perpendicular to y = -5x + 2?
Homework
96) What is a line parallel to y = 3/8x + 4?
97) What is a line parallel to y = -2x -7?
98) What is a line parallel to y = 3x?
99) What is a line parallel to y = 2?
100) What is a line perpendicular to y = -1/2x + 1?
101) What is a line perpendicular to y = 3/7x -4?
102) What is a line perpendicular to y = 9x?
103) What is a line perpendicular to y = -11/2x - 16?
Systems: Solve by graphing Classwork
104) y = -x – 7
y = x – 7
105) y = - x + 2
y = - x + 3
106) y = -3x – 5
y = x + 3
107) y = -2x + 5
y = x – 2
108) y = -4x + 7
y = -3x + 3
109) y = x – 3
y = x + 2
110) y = x + 3
y = - x – 3
111) y = x + 2
y = -x – 2
112) y = 4x – 1
y = -x + 4
113) y = 3x – 4
y = 4x + 10
Systems: Solve by graphing Homework
114) y = - x – 4
y = - x + 1
115) y = -2x – 2
y = -3x – 6
116) y = x – 2
y = x + 2
117) y = x + 1
y = - x – 4
118) y = x – 4
y = -x + 2
119) y = -4x – 1
y = x – 11
120) y = -3x – 3
y = x + 4
121) y = - x + 3
y = x – 1
122) y = -x – 2
y = - x + 2
123) y = x + 5
y = -x + 3
Systems: Solve by Substitution Classwork
124) x = 4y – 9
x = y + 3
125) 5x = -2y + 48
x = -3y + 20
126) y – 4x = 28
y = -2x – 2
127) y + 2x = -12
y = x + 15
128) x = -2y – 7
2x + y = -14
129) x = 5y – 38
x = -4y + 16
130) y = 2x + 3
4x – 2y = 8
131) x = -4y + 8
x = 3y + 8
132) 5y + 5x = 85
y = 4x – 18
133) x = y – 12
x = 5y – 40
Systems: Solve by Substitution Homework
134) y = -5x + 41
-2x = -14 – 2y
135) y = 3x + 6
-6x + 2y = 12
136) y – 3x = 0
y = -3x – 18
137) x = -3y + 13
4x – 4y = 20
138) x = -4y + 29
5x + 2y = 37
139) y = -2x + 11
5y – 2x = 31
140) 5y – 5x = -15
y = -3x + 29
141) -4x = 3y + 32
x = -5y – 8
142) y = -3x – 1
-4y + x = -9
143) y = -4x + 17
-3y – x = -7
Systems: Solve by Elimination (Addition & Subtraction) Classwork
144) 3x + y = 36
5x + y = 56
145) x + 2y = 25
x + 3y = 33
146) 3x – 5y = -52
x – 5y = -34
147) 2x + 3y = 4
-2x + 5y = 60
148) 2x + 2y = 2
5x – 2y = 40
149) -x + 2y = 14
x – 2y = -11
150) 4x – y = 16
4x + 2y = 16
151) 2x + 5y = 5
-2x + y = -23
152) 2x – 2y = -12
x – 2y = -13
153) 5x + 5y = 40
-5x + 3y = -40
Systems: Solve by Elimination (Addition & Subtraction) Homework
154) 4x – y = -2
4x + 5y = 10
155) 2x + 4y = 10
-4x + 4y = 52
156) -3x – 5y = 49
3x + 4y = -44
157) -4x + 3y = 39
5x – 3y = -45
158) -5x – 2y = -5
-x – 2y = -1
159) x + 5y = -4
-x + 2y = -10
160) -4x + 2y = -44
4x + 4y = 20
161) x + 2y = 4
x + 5y = -2
162) 3x – y = -5
-3x – 2y = -10
163) 3x – y = 11
-3x – 5y = -71
Systems: Solve by Elimination (Multiply First)
Classwork
164) 5x – 4y = 47
-x – 16y = 125
165) 3x – 2y = 33
-4x – 4y = 16
166) 2x + y = 21
4x + 3y = 51
167) -3x + 3y = -27
12x + 5y = 108
168) 3x + 4y = 3
-12x – y = -57
169) 2x + 5y = -7
8x + 3y = 57
170) 4x + 3y = 33
8x + y = 31
171) 3x + 3y = 31
-9x – 5y = -67
172) –x – y = -8
-4x + 2y = 22
173) 2x + y = 0
-8x + 4y = 80
Homework
174) –x + y = -5
-3x + 4y = -12
175) -2x – y = 2
-6x + 3y = -18
176) -2x + 2y = 16
6x – y = -13
177) -4x – 5y = -9
3x + 10y = 13
178) 3x – 2y = -26
6x – 4y = -70
179) x + 5y = -12
3x + y = 6
180) x + y = 14