MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Plot the points on the Cartesian coordinate system provided. 1) A(5, 5), B(-4, 3) 8
y
8 x
-8
-8
A) 8
y A B
8 x
-8
-8
B) 8
y A
B
8 x
-8
-8
1
C) 8
y A
8 x
-8 B
-8
D) 8
y
A B
8 x
-8
-8
Answer: B 2) A(2, -6), B(-1, 2) 8
y
8 x
-8
-8
2
A) 8
y
B
8 x
-8
A -8
B) 8
y A
B
8 x
-8
-8
C) 8
y A
B
8 x
-8
-8
3
D) 8
y
B
8 x
-8
A -8
Answer: D 3) A(-6, -4), B(-1, 1) 8
y
8 x
-8
-8
A) 8
y
A
B 8 x
-8
-8
4
B) 8
y
B 8 x
-8 A
-8
C) 8
y
A
B 8 x
-8
-8
D) 8
y
B 8 x
-8 A
-8
Answer: D
5
4) A(1, 3), B(3, -5) y
8
8 x
-8
-8
A) 8
y
B
A 8 x
-8
-8
B) 8
y
A
8 x
-8
B
-8
6
C) 8
y B A
8 x
-8
-8
D) 8
y
A
8 x
-8
B
-8
Answer: D 5) A(2, 5), B(-4, -3) 8
y
8 x
-8
-8
7
A) 8
y
B
8 x
-8
A
-8
B) 8
y A B
8 x
-8
-8
C) 8
y A
8 x
-8 B
-8
8
D) 8
y
8 x
-8 B A
-8
Answer: C 6) A(-
4 , -2), B(-4, 6) 5 8
y
8 x
-8
-8
A) 8
y
B
-8
A
8 x
-8
9
B) 8
y B
-8
8 x
A
-8
C) 8
y
B
-8
8 x
A
-8
D) 8
y
B
-8
A
8 x
-8
Answer: C
10
7) A(-2, 0), B (0, 6) 8
y
8 x
-8
-8
A) 8
y
B 8 x
-8 A
-8
B) 8
y B
8 x
-8 A
-8
11
C) 8
y B
A 8 x
-8
-8
D) 8
A
y
B 8 x
-8
-8
Answer: C Give the coordinates for the points labeled on the graph. 8) y B A
x
A) A(7, 4); B(-3, 5) B) A(7, 4); B(5, -3) C) A(4, 30); B(5, -3) D) A(7, 5); B(4, 5) Answer: A
12
9) y
C
x D
A) C(-6, 2); D(-3, 2) B) C(2, 4); D(-3, 2) C) C(-6, 2); D(2, -3) D) C(-6, -3); D(2, -3) Answer: C 10) y
E
x G
A) E(2, 10); G(-2, -6) B) E(-3, -2); G(2, -2) C) E(-3, 2); G(-2, -6) D) E(-3, 2); G(-6, -2) Answer: D
13
11) y
A
x
B
A) A(2, -2); B(1, -4) B) A(2, 2); B(0, -4) C) A(-2, 2); B(0, 4) D) A(2, 2); B(0, 4) Answer: B 12) Determine which of the following points lie on the graph of the linear equation 4x + 5y = 20. A) (-5, 8) B) (5, 4) C) (0, -4) D) (-4, 20) E) (0, 0) Answer: A SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 13) On the line 2y = 6, is there a point whose first coordinate is 4? If so, name the point. Answer: (4, 3) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine if the given point is on the graph of the equation. 14) 4x + 5y = 8; (0, 2) A) No B) Yes Answer: A 15)
3 x + y = 1; (-4, 4) 4 A) Yes B) No Answer: A
14
16) -
2 x + y = -1; (-1, 0) 3 A) No B) Yes
Answer: A The equation is in the form y = mx + b. Identify m and b. 5 9 17) y = x 2 2 A) m =
5 9 ;b=2 2
B) m =
5 9 ;b= 2 2
C) m = D) m =
9 5 ;b= 2 2
9 5 ;b= 2 2
Answer: A 18) y = x - 6 A) m = -6; b = 1 B) m = 1; b = -6 C) m = -6; b = -1 D) m = 0; b = 6 Answer: B 19) y = -4x - 5 A) m = -4; b = -5 B) m = 5; b = -4 C) m = -5; b = -4 D) m = -4; b = 5 Answer: A 20) y = 15 A) m = 15; b = 15 B) m = 15; b = 0 C) m = 0; b = 15 D) m = 0; b =0 Answer: C 21) Find the standard form of the linear equation x =3y - 4. 1 4 A) y = x + 3 3 B) x = y -4 C) x -3 y =- 4 D) 3y = -x + 4 E) none of these Answer: A
15
22) Find the standard form of the linear equation 4x - 7y = 14. 4 A) y = x - 2 7 B) 7y = -4x + 14 2 1 C) x - y = 1 7 2 D) 4x = 7y + 14 E) none of these Answer: A 23) Find the standard form of the equation -2x + 3y = 6. 2 A) y = x + 6 3 B) y = -
2 x+6 3
C) y = -
2 x+2 3
D) y =
2 x+2 3
E) none of these Answer: D SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 24) Write the equation of the line x +3y = 1 in standard form. Answer: y = -
1 1 x+ 3 3
25) Write the equation of the line -4x + 2y = 5 in standard form. Answer: y = 2x +
5 2
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 26) Which of the following equations describe the same line as the equation 3x + 4y = 5? 3 A) y = x + 5 4 B) 5 - 3x - 4y = 0 C) 6x + 8y = 5 3 5 D) y = x + 4 4 E) none of these Answer: B
16
Write the equation in slope-intercept form. 27) 16x + 10y = 5 A) y = 16x - 5 8 1 B) y = x 5 2 C) y = D) y =
8 1 x+ 5 2
8 1 x+ 5 2
Answer: C 28) 4x - 8y = 7 1 7 A) y = x + 2 8 B) y = 2x +
7 4
C) y = 4x - 7 1 7 D) y = x 2 8 Answer: D 29) x - 5y = 9 A) y = 5x - 9 B) y = x -
9 5
C) y =
1 9 x5 5
D) y =
1 x-9 5
Answer: C 30) Find the x-intercept of the line y = 8x - 12. 3 A) , 0 2 B) (8, 0) C) (0, -12) 3 D) 0, 2 E) none of these Answer: A
17
31) Find the x-intercept of the line y = 2x + 5. 5 A) - , 0 2 B) (0, 5) C) (5, 0) D) 0, -
5 2
E) none of these Answer: A 32) Find the y-intercept of the line y = 0.5x + 4. A) (0, 4) B) (1, 0) C) (4, 0) D) (0, 1) E) none of these Answer: A 33) Find the y-intercept of the line x-y = 3. A) (3, 0) B) (0, 3) C) (-3, 0) D) (0, -3) E) none of these Answer: D 34) Find the y-intercept of the line 2y -x =6. A) (3, 0) B) (-6, 0) C) (0, 3) D) (0,-6) E) none of these Answer: C 35) Find the y-intercept of the line y = 0.5x + 4. A) (1, 0) B) (0, 4) C) (4, 0) D) (0, 1) E) none of these. Answer: B SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 36) Find the x-intercept and y-intercept for the line y = -2x + 6. Answer: x-intercept: (3, 0) y-intercept: (0, 6) 37) Find the x-intercept and y-intercept for the line y = 2. Answer: x-intercept: none y-intercept: (0, 2) 18
38) Find the x-intercept and y-intercept for the line x = -3. Answer: x-intercept: (-3, 0) y-intercept: none 39) Find the x-intercept and y-intercept for the line y = 5x. Answer: x-intercept: (0, 0) y-intercept: (0, 0) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 40) The coordinates of the x-intercept are the same as the coordinates of the y-intercept on the graph of the line whose equation is A) x - 3y = 0 B) 2x + y = 2 C) 2x + 2y = 8 D) 2x - 3y = 3 E) none of these Answer: A Find the intercepts for the equation. 41) y = -x + 5 A) x-intercept: (2, 0); y-intercept: (0, 3) B) x-intercept: (0, 0); y-intercept: (0, 5) C) x-intercept: (5, 0); y-intercept: (0, 5) D) x-intercept: (5, 0); y-intercept: (0, -5) Answer: C Find the x- and y-intercepts for the equation. 42) y = 5x - 3 3 A) x-intercept: , 0 , y-intercept: (0, -3) 5 B) x-intercept: (-3, 0) , y-intercept: 0, C) x-intercept:
3 5
3 , 0 , y-intercept: (0, 3) 5
D) x-intercept: -
3 , 0 , y-intercept: (0, -3) 5
Answer: A 43) y = 5x A) x-intercept: (0, 0), y-intercept: (0, 0) 1 B) x-intercept: (0, 0), y-intercept: (0, ) 5 C) x-intercept: (5, 0), y-intercept: (0, 0) D) x-intercept: (-5, 0), y-intercept: (0, 0) Answer: A
19
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Sketch the graph of the linear equation. Label the coordinates of the y-intercept and the x-intercept. 44) 2x - 5y = -10 y 10
5
-10
-5
5
10
x
-5
-10
Answer: y 10
5 (0, 2) (-5, 0) -10
-5
5
10
x
-5
-10
20
45) y = -2x + 3 y 10
5
-10
-5
5
10
x
-5
-10
Answer: y 10
5 (0, 3) (3/2, 0) -10
-5
5
10
x
-5
-10
21
46) 3y +2x = 6 y 10
5
-10
-5
5
10
x
-5
-10
Answer: y 10
5 (0, 2) -10
-5
(3, 0) 5
10
x
-5
-10
22
47) 5x - 10y = 20 y 10
5
-10
-5
5
10
x
-5
-10
Answer: y 10
5 (4, 0) -10
-5
5
10
x
(0, -2) -5
-10
23
48) y - 3x = 0 y 10
5
-10
-5
5
10
x
-5
-10
Answer: y 10
5 (0, 0) -10
-5
5
10
x
-5
-10
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the equation. 1 49) y = - x - 4 2 y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
8 10
x
-4 -6 -8 -10
24
A) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
8
10
x
2
4
6
8
10
x
2
4
6
8
10
x
-4 -6 -8 -10
B) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2 -4 -6 -8 -10
C) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2 -4 -6 -8 -10
25
D) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
6
8 10
2
4
8
10
x
10
x
-4 -6 -8 -10
Answer: C 50) 5y + 7x = 5 y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
x
-4 -6 -8 -10
A) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
6
8
-4 -6 -8 -10
26
B) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
8
10
x
2
4
6
8
10
x
2
4
6
8
10
x
-4 -6 -8 -10
C) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2 -4 -6 -8 -10
D) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2 -4 -6 -8 -10
Answer: B
27
51) 4x - 20y = 0 y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
x
6
8 10
2
4
6
8
10
x
2
4
6
8
10
x
-4 -6 -8 -10
A) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2 -4 -6 -8 -10
B) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2 -4 -6 -8 -10
28
C) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
8
10
x
2
4
6
8
10
x
6
8 10
-4 -6 -8 -10
D) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2 -4 -6 -8 -10
Answer: C 52) x = -2 y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
x
-4 -6 -8 -10
29
A) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
8
10
x
2
4
6
8
10
x
2
4
6
8
10
x
-4 -6 -8 -10
B) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2 -4 -6 -8 -10
C) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2 -4 -6 -8 -10
30
D) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
6
8 10
2
4
8
10
x
10
x
-4 -6 -8 -10
Answer: C 53) y = 4 y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
x
-4 -6 -8 -10
A) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
6
8
-4 -6 -8 -10
31
B) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
8
10
x
2
4
6
8
10
x
2
4
6
8
10
x
-4 -6 -8 -10
C) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2 -4 -6 -8 -10
D) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2 -4 -6 -8 -10
Answer: B Graph the linear equation.
32
54) y = 4x y 10
5
-10
-5
5
10
x
-5
-10
A) y 10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
B) y 10
5
-10
-5 -5
-10
C) y 10
5
-10
-5 -5
-10
33
D) y 10
5
-10
-5
10
x
5
10
x
5
10
x
5 -5
-10
Answer: A Choose the graph that matches the equation. 55) 2x - y = 4 A) y 10
5
-10
-5 -5
-10
B) y 10
5
-10
-5 -5
-10
34
C) y 10
5
-10
-5
5
10
x
5
10
x
-5
-10
D) y 10
5
-10
-5 -5
-10
Answer: C
35
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 56) The value y of a machine (in dollars) is known to depreciate linearly with time x (measured in years from the time it was bought new). Suppose that y is related to x by the equation y = 2000 - 200x. (a) Sketch the graph of this linear equation for 0 ≤ x ≤ 10. (b) What is the value of the machine when it is 5 years old? (c) What is the economic interpretation of the y-intercept of the graph? (d) When will the value of the machine reach the scrap value of $400? y
x
Answer: (a) y 2000
10
x
(b) $1000 (c) the value of the machine when it is new (d) 8 years
36
57) A towing company charges a fixed amount in addition to a per-mile charge to tow a car. The total charge y in dollars is related to the towing distance x in miles by the equation y = 30 + 2x. (a) Sketch the graph of this equation for 0 ≤ x ≤ 25. (b) What is the charge of towing a car for 15 miles? (c) If the company charged a customer $50 to tow his car, what was the corresponding towing distance? y 100 80 60 40 20
5
10
15
20
25 x
5
10
15
Answer: (a) y 100 80 60 40 20
20
25 x
(b) $60 (c) 10 miles
37
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 58) The value, v, in hundreds of dollars, of Juan's television is approximated by v = -0.50t + 8, where t is the number of years since he first bought the television. Graph the equation and use the graph to estimate the value of the television 4 years after it was purchased. v
1000 900 800 700 600 500 400 300 200 100
1
2
3
4
5
6
7
8
9 t
A) $720 B) $600 C) $400 D) $1000 Answer: B 59) During the month of January, the depth, d, of snow in inches at the base of one ski resort could be approximated by d = -2t + 68, where t is the number of days since December 31st. Graph the equation and use the graph to estimate the depth of snow on January 28th. d 65 60 55 50 45 40 35 30 25 20 15 10 5 4
8
12 16 20 24 28 32 t
A) 20 in. B) 17 in. C) 12 in. D) 40 in. Answer: C
38
60) The cost, T, in hundreds of dollars, of tuition at one community college is given by T = 3 + 1.25c, where c is the number of credits for which a student registers. Graph the equation and use the graph to estimate the cost of tuition if a student registers for 8 credits. 20 18 16 14 12 10 8 6 4 2
T
1 2 3 4 5 6 7 8 9 10 11 c
A) $2200 B) $1800 C) $1000 D) $1300 Answer: D Find an equation for the line with the given conditions. 61) y-intercept (0, 7), x-intercept (-6, 0) 6 A) y = x - 6 7 B) y =
7 x+7 6
C) y = -
7 x+7 6
D) y = -
6 x-6 7
Answer: B The general form of the equation of a line is cx + dy = e, where not both c and d are 0. Find the general form of the equation. 62) y = 9x + 5 A) -9x - y = 5 5 B) x - y = 9 C) 9x - y = -5 D) 9x + y = 5 Answer: C 63) y =
2 x-5 3
A) 2x + 3y = 10 B) 3x - 2y = -15 C) 2x - 3y = 15 D) 2x + 3y = -5 Answer: C
39
64) Find the slope of the line 3x - 2y + 12 = 0. A) -2 3 B) 2 C) -
2 3
D) 3 E) none of these Answer: B 65) Find the slope of the line x= -2. A) undefined 1 B) 2 C) -2 D) 0 E) none of these Answer: A 66) Find the slope of the line y = 3. A) 0 B) 1 C) 3 1 D) 3 E) none of these Answer: A 67) Find the slope of the line y - 2 = 3(x + 5). 3 A) 2 B) -2 C) 3 3 D) 2 E) none of these Answer: C 68) Find the slope of the line y + 3 = -(x - 2). A) 1 B) -1 3 C) 2 D) 3 E) none of these Answer: B
40
69) Find the slope of the line 5y + 7x - 43 = 0. 7 A) 5 B) 7 43 C) 5 D) -7 E) none of these Answer: A 70) Find the slope of the line passing through the points (2, 0) and (2, 6). A) 4 B) 0 2 C) 3 D) undefined E) none of these Answer: D 71) Find the slope of the line passing through the points (2, -5) and (-1, 3). 8 A) 3 B) -
2 5
C) -
3 8
D) -
5 2
E) none of these Answer: A Find the slope of the line. 72) y = 2x + 1 A) -2 B) 1 C) 2 D) -1 Answer: C 73) 2x + 5y = 26 2 A) 5 B) C)
2 5
5 2
D) -
5 2
Answer: B 41
74) 4x - 5y = 18 4 A) 5 B)
5 4
C) D)
5 4
4 5
Answer: D 75) y = -2 A) 2 B) 0 C) -2 D) undefined Answer: B Graph the line containing the given pair of points and find the slope. 76) (-6, 0) (0, -1) y 10
5
-10
-5
5
10
x
-5
-10
A)
1 6 y 10
5
-10
-5
5
10
x
-5
-10
42
B) -
1 6 y 10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
C) 6 y 10
5
-10
-5 -5
-10
D) -6 y 10
5
-10
-5 -5
-10
Answer: B
43
77) (1, 7) (0, 0) y 10
5
-10
-5
5
10
x
-5
-10
A)
1 7 y 10
5
-10
-5
5
10
x
5
10
x
-5
-10
B) -
1 7 y 10
5
-10
-5 -5
-10
44
C) -7 y 10
5
-10
-5
5
10
x
5
10
x
-5
-10
D) 7 y 10
5
-10
-5 -5
-10
Answer: D 78) (2, -8) (-1, 4) y 10
5
-10
-5
5
10
x
-5
-10
45
A)
1 4 y 10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
B) -
1 4 y 10
5
-10
-5 -5
-10
C) - 4 y 10
5
-10
-5 -5
-10
46
D) 4 y 10
5
-10
-5
5
10
x
-5
-10
Answer: C 79) (3, 2) (-4, 2) y 10
5
-10
-5
5
10
x
-5
-10
A) 0 y 10
5
-10
-5
5
10
x
-5
-10
47
B) 1 y 10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
C) 1 y 10
5
-10
-5 -5
-10
D) 0 y 10
5
-10
-5 -5
-10
Answer: A Graph the line on the coordinate plane using the given information.
48
80) Passes through (0, 4) and m =
1 2
y 10
5
-10
-5
5
10
x
-5
-10
A) y 10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
B) y 10
5
-10
-5 -5
-10
C) y 10
5
-10
-5 -5
-10
49
D) y 10
5
-10
-5
5
10
x
10
x
-5
-10
Answer: B 81) Passes through (-2, -10) and m = 6 y 10
5
-10
-5
5
10
x
-5
-10
A) y 10
5
-10
-5
5 -5
-10
50
B) y 10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
C) y 10
5
-10
-5 -5
-10
D) y 10
5
-10
-5 -5
-10
Answer: C
51
82) Passes through (0, 5) and m = - 2 y 10
5
-10
-5
5
10
x
-5
-10
A) y 10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
B) y 10
5
-10
-5 -5
-10
C) y 10
5
-10
-5 -5
-10
52
D) y 10
5
-10
-5
5
10
x
10
x
-5
-10
Answer: C 83) Passes through (0, 3) and m = -
1 2
y 10
5
-10
-5
5
10
x
-5
-10
A) y 10
5
-10
-5
5 -5
-10
53
B) y 10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
C) y 10
5
-10
-5 -5
-10
D) y 10
5
-10
-5 -5
-10
Answer: D
54
84) Passes through (10, 0) and m = -
1 5
y 10
5
-10
-5
5
10
x
-5
-10
A) y 10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
B) y 10
5
-10
-5 -5
-10
C) y 10
5
-10
-5 -5
-10
55
D) y 10
5
-10
-5
5
10
x
10
x
-5
-10
Answer: A 85) Passes through (0, 2) and m = -
1 6
y 10
5
-10
-5
5
10
x
-5
-10
A) y 10
5
-10
-5
5 -5
-10
56
B) y 10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
C) y 10
5
-10
-5 -5
-10
D) y 10
5
-10
-5 -5
-10
Answer: C
57
86) Passes through (3, 9) and m = 0 y 10
5
-10
-5
5
10
x
-5
-10
A) y 10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
B) y 10
5
-10
-5 -5
-10
C) y 10
5
-10
-5 -5
-10
58