Chapter 2 - Linear Equations in Two Variables and Functions
Chapter 2 - Linear Equations in Two Variables and Functions
1. Plot the point on the rectangular coordinate system.
(–3, –2)
A)
B)
C)
D)
Ans:A Concept:PlottingPoints Difficulty:Easy Section:2.1
2. Plot the point on the rectangular coordinate system.
A)
B)
C)
D)
Ans:C Concept:PlottingPoints Difficulty:Easy Section:2.1
3. Plot the point on the rectangular coordinate system.
(3.2, 2.7)
A)
B)
C)
D)
Ans:D Concept:PlottingPoints Difficulty:Easy Section:2.1
4. Give the coordinates of the specified point.
point VI
A) B) C) D)
Ans:B Concept:PlottingPoints Difficulty:Easy Section:2.1
5. Determine if the ordered pair is a solution to the linear equation.
–3x – 4y = 44 ; (–4, –8)
A) Yes B) No
Ans:A Concept:LinearEquationsinTwoVariables Difficulty:Easy Section:2.1
6. Determine if the ordered pair is a solution to the linear equation.
8x + 3y = 82 ; (9, 4)
A) Yes B) No
Ans:B Concept:LinearEquationsinTwoVariables Difficulty:Easy Section:2.1
7. Determine if the ordered pair is a solution to the linear equation.
; (9, 1)
A) Yes B) No
Ans:A Concept:LinearEquationsinTwoVariables Difficulty:Easy Section:2.1
8. Determine if the ordered pair is a solution to the linear equation.
; (28, 36)
A) Yes B) No
Ans:B Concept:LinearEquationsinTwoVariables Difficulty:Easy Section:2.1
9. Complete the table. Then graph the line defined by the points.
9x + 2y = 6
Ans:
Concept:Graphing Linear Equations in Two Variables Difficulty:Moderate Section:2.1
10. Graph the linear equation.
y = –3x – 2
A)
B)
C)
D)
Ans:C Concept:Graphing Linear Equations in Two Variables Difficulty:Moderate Section:2.1
11. Graph the linear equation.
A)
B)
C)
D)
Ans:D Concept:Graphing Linear Equations in Two Variables Difficulty:Moderate Section:2.1
12. Graph the linear equation.
x = 3y – 2
A)
B)
C)
D)
Ans:A Concept:Graphing Linear Equations in Two Variables Difficulty:Moderate Section:2.1
13. Graph the linear equation.
2y = 3x – 6
A)
B)
C)
D)
Ans:B Concept:Graphing Linear Equations in Two Variables Difficulty:Moderate Section:2.1
14. Find the x-intercept and the y-intercept.
A) x-intercept: ; y-intercept:
B) x-intercept: ; y-intercept:
C) x-intercept: ; y-intercept:
D) x-intercept: ; y-intercept:
Ans:B Concept:x-Interceptsandy-Intercepts Difficulty:Moderate Section:2.1
15. Find the x-intercept and the y-intercept.
A) x-intercept: ; y-intercept:
B) x-intercept: ; y-intercept:
C) x-intercept: ; y-intercept:
D) x-intercept: ; y-intercept:
Ans:D Concept:x-Interceptsandy-Intercepts Difficulty:Moderate Section:2.1
16. Find the x-intercept and the y-intercept.
A) x-intercept: ; y-intercept:
B) x-intercept: ; y-intercept:
C) x-intercept: ; y-intercept:
D) x-intercept: ; y-intercept:
Ans:A Concept:x-Interceptsandy-Intercepts Difficulty:Moderate Section:2.1
17. Find the x-intercept and the y-intercept and graph both. Then graph the line.
–2x – 5y = 20
A)
B)
C)
D)
Ans:D Concept:x-Interceptsandy-Intercepts Difficulty:Moderate Section:2.1
18. Find the x-intercept and the y-intercept and graph both. Then graph the line.
A)
B)
C)
D)
Ans:C Concept:x-Interceptsandy-Intercepts Difficulty:Moderate Section:2.1
19. A manufacturing company produces plastic pipe used in wastewater treatment applications. The pipe measures 4 inches in diameter and is cut to 10-foot lengths. The manufacturer's fixed costs are $10,000 per month (The fixed cost is the cost to operate the company even if it produces no pipe. It includes rent, debt payments, salaries, etc.). It costs an additional $1.40 for each unit of pipe produced. The overall monthly production costs are described by the linear equation
where y represents the total monthly operating cost and x represents the number of units of pipe produced.
What does the y-intercept mean in the context of this problem?
A) The y-intercept represents the increase in total cost when production is increased by one unit of pipe.
B) The y-intercept represents the fixed cost of $10,000.
C) The y-intercept indicates that the fixed cost increases by $10,000 per month.
D) The y-intercept represents the cost ($1.40) per unit of pipe.
Ans:B Concept:x-Interceptsandy-Intercepts Difficulty:Easy Section:2.1
20. Identify the line as either vertical or horizontal, and graph the line.
y = –3
A) Vertical
B) Vertical
C) Horizontal
D) Horizontal
Ans:C Concept:HorizontalandVerticalLines Difficulty:Easy Section:2.1
21. Identify the line as either vertical or horizontal, and graph the line.
2y – 9 = –3
A) Vertical
B) Vertical
C) Horizontal
D) Horizontal
Ans:C Concept:HorizontalandVerticalLines Difficulty:Easy Section:2.1
22. Which of the lines defined here have only one unique intercept?
a. x = 7
b. 7x + 4y = –5
c. 2y = 7
d. –9x – 5y = 0
A) b. B) a. and c. C) b., and d D) a., c., and d.
Ans:D Concept:x-Interceptsandy-Intercepts Difficulty:Easy Section:2.1
23. A metal mast is stabilized with 3 guy wires (see figure). Find the slope of one of the guy wires if d = 90 feet and h = 80 ft.
[The figure is not necessarily drawn to scale.]
A) B) C) D) 120
Ans:C Concept:IntroductiontotheSlopeofaLine Difficulty:Easy Section:2.2
24. Find the slope of the hill.
/ 14 yd247 yd
[The figure is not necessarily drawn to scale.]
A) B) C) D) 247
Ans:A Concept:IntroductiontotheSlopeofaLine Difficulty:Easy Section:2.2
25. If a plane loses 1100 feet in altitude over a horizontal distance of 15,000 feet, what is the slope?
A) B) C) D)
Ans:A Concept:IntroductiontotheSlopeofaLine Difficulty:Easy Section:2.2
26. Use the slope formula to determine the slope of the line containing the two points.
A) B) C) D)
Ans:D Concept:TheSlopeFormula Difficulty:Easy Section:2.2
27. Use the slope formula to determine the slope of the line containing the two points.
A) B) C) D)
Ans:B Concept:TheSlopeFormula Difficulty:Easy Section:2.2
28. Use the slope formula to determine the slope of the line containing the two points. Round to the nearest hundredth.
A) –3 B) 0.3 C) –0.33 D) –1.24
Ans:A Concept:TheSlopeFormula Difficulty:Easy Section:2.2
29. Use the slope formula to determine the slope of the line containing the two points.
A) 0 B) C) D) undefined
Ans:D Concept:TheSlopeFormula Difficulty:Easy Section:2.2
30. Use the slope formula to determine the slope of the line containing the two points.
A) 0 B) C) D) undefined
Ans:A Concept:TheSlopeFormula Difficulty:Easy Section:2.2
31. Use the slope formula to determine the slope of the line containing the two points.
A) B) C) D)
Ans:A Concept:TheSlopeFormula Difficulty:Easy Section:2.2
32. Estimate the slope of the line from its graph.
A)
B)
C)
D)
Ans:C Concept:TheSlopeFormula Difficulty:Moderate Section:2.2
33. The slope of a line is given. Find the slope of a line parallel to the given line.
A) – B) C) D) –
Ans:B Concept:ParallelandPerpendicularLines Difficulty:Easy Section:2.2
34. The slope of a line is given. Find the slope of a line perpendicular to the given line.
A) – B) C) D) –
Ans:D Concept:ParallelandPerpendicularLines Difficulty:Easy Section:2.2
35. Two points are given from each of two lines L1 and L2. Without graphing the points, determine if the lines are perpendicular, parallel, or neither.
L1:
L2:
A) Perpendicular B) Parallel C) Neither
Ans:B Concept:ParallelandPerpendicularLines Difficulty:Moderate Section:2.2
36. Two points are given from each of two lines L1 and L2. Without graphing the points, determine if the lines are perpendicular, parallel, or neither.
L1:
L2:
A) Perpendicular B) Parallel C) Neither
Ans:A Concept:ParallelandPerpendicularLines Difficulty:Moderate Section:2.2
37. Two points are given from each of two lines L1 and L2. Without graphing the points, determine if the lines are perpendicular, parallel, or neither.
L1:
L2:
A) Perpendicular B) Parallel C) Neither
Ans:C Concept:ParallelandPerpendicularLines Difficulty:Moderate Section:2.2
38. The graph shows the enrollment at Riverside Community College for selected years. Use the coordinates of the given points to find the slope of the line. Interpret the meaning of the slope in the context of this problem.
A) m = 250; Enrollment increases by an approximate factor of 250 students per year.
B) m = 125; Enrollment increases by an approximate factor of 125 students per year.
C) m = 250; Enrollment increases by approximately 250 students per year.
D) m = 125; Enrollment increases by approximately 125 students per year.
Ans:D Concept:Applications and Interpretation of Slope Difficulty:Moderate Section:2.2
39. Determine the slope and the y-intercept of the line.
72 = 8y
A) Slope: 0; y-intercept: (0, 9) C) Slope: 1; y-intercept: (0, 9)
B) Slope: 0; y-intercept: (9, 0) D) Slope: undefined; y-intercept: (9, 0)
Ans:A Concept:Slope-InterceptForm Difficulty:Easy Section:2.3
40. Determine the slope and the y-intercept of the line.
A) Slope: C) Slope:
B) Slope: D) Slope:
Ans:B Concept:Slope-InterceptForm Difficulty:Easy Section:2.3
41. Determine the slope and the y-intercept of the line. Round your answer to three decimal place, if necessary.
A) Slope: 0.455; y-intercept: (0, 1.25) C) Slope: –1.25; y-intercept: (0, 2.2)
B) Slope: 2.2; y-intercept: (0, 1.25) D) Slope: 2.2; y-intercept: (0, –1.25)
Ans:B Concept:Slope-InterceptForm Difficulty:Easy Section:2.3
42. Match the equation with the correct graph below.
A)
B)
C)
D)
Ans:D Concept:Slope-InterceptForm Difficulty:Moderate Section:2.3
43. Match the equation with the correct graph below.
x = 2
A)
B)
C)
D)
Ans:B Concept:Slope-InterceptForm Difficulty:Moderate Section:2.3
44. Write the equation in slope-intercept form. Then graph the line using the slope and y-intercept.
3x = –2 – y
A) y = –3x – 2
B) y = –3x + 2
C) y = 3x + 2
D) y =3x – 2
Ans:A Concept:Slope-InterceptForm Difficulty:Moderate Section:2.3
45. Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept.
2x – 3y = 6
A)
B)
C)
D)
Ans:C Concept:Slope-InterceptForm Difficulty:Moderate Section:2.3
46. Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept.
4x + 3y = 0
A)
B)
C)
D)
Ans:A Concept:Slope-InterceptForm Difficulty:Moderate Section:2.3
47. Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.
A) parallel B) perpendicular C) neither
Ans:A Concept:Slope-InterceptForm Difficulty:Easy Section:2.3
48. Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.
A) parallel B) perpendicular C) neither
Ans:B Concept:Slope-InterceptForm Difficulty:Easy Section:2.3
49. Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.
A) parallel B) perpendicular C) neither
Ans:C Concept:Slope-InterceptForm Difficulty:Easy Section:2.3
50. Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.
A) parallel B) perpendicular C) neither
Ans:A Concept:Slope-InterceptForm Difficulty:Easy Section:2.3
51. Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.
A) parallel B) perpendicular C) neither
Ans:B Concept:Slope-InterceptForm Difficulty:Easy Section:2.3
52. Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.
A) parallel B) perpendicular C) neither
Ans:C Concept:Slope-InterceptForm Difficulty:Easy Section:2.3
53. Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.
A) parallel B) perpendicular C) neither
Ans:A Concept:Slope-InterceptForm Difficulty:Easy Section:2.3
54. Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.
A) parallel B) perpendicular C) neither
Ans:B Concept:Slope-InterceptForm Difficulty:Easy Section:2.3
55. Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.
A) parallel B) perpendicular C) neither
Ans:C Concept:Slope-InterceptForm Difficulty:Easy Section:2.3
56. Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept from.
The line passes through the point and has a slope of –4.
A) y = –4x + 10 B) y = –4x – 3 C) y = –4x – 2 D) y = 4x + 10
Ans:C Concept:ThePoint-SlopeFormula Difficulty:Moderate Section:2.3
57. Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept from.
The line passes through the point and has a slope of .
A) B) C) D)
Ans:A Concept:ThePoint-SlopeFormula Difficulty:Moderate Section:2.3
58. Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept from.
The line passes through (2, 3) and (3, 5).
A) y = 2x – 1 B) y = 8x – 1 C) y = 2x + 1 D) y = 8x + 1
Ans:A Concept:ThePoint-SlopeFormula Difficulty:Moderate Section:2.3
59. Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept from.
The line passes through (7, 5) and (5, 13).
A) y = –4x – 33 B) y = –4x + 23 C) y = 4x + 23 D) y = –4x + 33
Ans:D Concept:ThePoint-SlopeFormula Difficulty:Moderate Section:2.3
60. Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept from.
The line passes through (10, 4) and (10, –11).
A) x = 10 B) y = 10 C) D)
Ans:A Concept:ThePoint-SlopeFormula Difficulty:Moderate Section:2.3
61. Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept from.
The line passes through (–3, –9) and (–5, –9).
A) y = –9 B) x = –9 C) y = 9 D) y = –9x
Ans:A Concept:ThePoint-SlopeFormula Difficulty:Moderate Section:2.3
62. Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept from.
The line contains the point and is parallel to a line with a slope of .
A) B) C) D)
Ans:A Concept:ThePoint-SlopeFormula Difficulty:Moderate Section:2.3
63. Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept from.
The line contains the point and is perpendicular to a line with a slope of .
A) B) C) D)
Ans:A Concept:ThePoint-SlopeFormula Difficulty:Moderate Section:2.3
64. Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept from.
The line contains the point (1, 20) and is parallel to 2y – 6x = 12.
A) y = 6x + 14 B) y = 3x + 17 C) 2y – 6x = 20 D) y = 3x + 6
Ans:B Concept:ThePoint-SlopeFormula Difficulty:Moderate Section:2.3
65. Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept from.
The line is perpendicular to the line defined by y = 3x – 8 and passes through the point (12, 3).
A) B) C) D)