M115 (Beginning Algebra)
Chapter 3 Practice Test
Name:
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the coordinates of the labeled points.
1)
1)
Determine the quadrant in which the point is located.
2) (-9, 18)
2)
3) (0, -2)
3)
Identify the quadrant with the given condition.
4) The first coordinate is positive.
4)
5) The second coordinate is negative.
5)
6) The coordinates have the same sign.
6)
7) The first and second coordinates have the opposite signs.
7)
Decide whether or not the ordered pair is a solution to the equation.
8) 4x - 5y = 18; (2, 2)
9) 2x + 3y = 25; (5, 5)
8)
9)
10) y = -3x; (1, -3)
10)
1
Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine
another solution. Answers may vary.
11) y = x - 2; (7, 5), (1, -1)
11)
12) x + 2y = 8; (6, 1), (-4, 6)
12)
Graph the equation.
13) y = 4x - 5
13)
2
14) 2x - y = -6
14)
Find the equation for the graph.
15)
15)
16)
16)
3
Find the coordinates of the y-intercept and the coordinates of all x-intercepts.
17)
18)
17)
18)
Find the intercepts for the equation.
19) 2x + y = 2
19)
20) -5x + 5y = 10
20)
21) y = 17
21)
22) x = 4
22)
4
Find the x- and y-intercepts for the equation. Then graph the equation.
23) 16y - 4x = -8
23)
24) y = -2x+ 6
24)
Graph the equation.
25) x - y = 6
25)
5
26) 8x = -56
26)
27) 48 + 6y = 0
27)
Write an equation for the graph.
28)
28)
6
29)
29)
Identify the missing units for the given rate.
30) If a student drove 427 miles in 7 hours, his average rate was 61
.
31) If a construction worker layed 52 bricks along a 26-foot driveway border, his average rate
was 2
.
Solve the problem.
32) To the nearest dollar, the average tuition at a public four-year college was $3106 in 1998
and $3430 in 1999. Find, to the nearest dollar per year, the rate at which tuition was
increasing.
30)
31)
32)
33) At 10:00 AM, Gavin rented a mountain bike. He returned the bike at 5:00 PM. He biked
for 45.5 miles. He paid $42.00 for the rental. Find the rental rate, in dollars per mile.
33)
34) The following graph shows data for a recent train ride from New York to Toronto. At what
rate did the train travel?
34)
Time of Day (PM)
7
Make the most appropriate graph to match the situation.
35) Joe runs until he reaches the shore of a lake. He then rows a boat to the other side of the
lake. He runs faster than he can row a boat.
36) In the morning Brenda drives away from home at a steady speed. She stops for breakfast.
She then continues to drive at a steady but faster speed.
Use the graph to solve the problem.
37) Find the rate of change in the temperature.
35)
36)
37)
8
38) Find the rate of change in Carlos's weight.
38)
months since start of diet
Find the slope of the line, or state that the slope is undefined if appropriate.
39)
40)
39)
40)
9
41) (3, 3) (3, -3)
41)
42) (-2, 1) (5, 1)
42)
Find the slope of the line containing the given pair of points. If the slope is undefined, state so.
43) (3, 2) and (-5, 9)
43)
44) (-7, -9) and (-7, 3)
44)
45) (7, 7) and (-7, 7)
45)
46) (2, 2) and (8, 11)
46)
Find the slope of the line. If the slope is undefined, state so.
47) x = -3
48) y = 4
47)
48)
10
Draw a line that has the given slope and y-intercept.
1
49) Slope - ; y-intercept (0, 3)
4
50) Slope
49)
1
; y-intercept (0, 4)
3
50)
Find the slope and the y-intercept of the line.
51) -6x + 8y = -8
52) y =
51)
15
x-5
4
52)
53) y - 8 = 3
53)
Find the slope-intercept equation for the line with the indicated slope and y-intercept.
5
54) Slope - ; y-intercept (0, 4)
8
55) Slope 4; y-intercept (0, 0)
54)
55)
11
Graph the linear equation.
3
56) y = - x - 3
4
56)
Determine whether the pair of equations represents parallel lines.
57) 3x - 8y = 13
32x + 12y = 13
57)
58) 9x + 3y = 12
6x + 2y = 9
58)
59) y = 3x - 5
9x + 3y = 6
59)
Write an equation in slope-intercept form of the line satisfying the given conditions.
60) Parallel to 4x - 7y = 29, y-intercept (0, -5)
60)
61) Perpendicular to 6x - 5y = 8 and the same y-intercept as 4x + 3y = 5.
61)
62) Through (-1, 12), parallel to -3x + 2y = 13
62)
63) Through (-8, 4), perpendicular to 9x - 8y = -40
63)
Determine whether the pair of equations represents perpendicular lines.
64) 4x - 6y = -5
36x + 12y = -5
65) 3x - 6y = -4
18x + 9y = -4
64)
65)
For the point-slope equation given, state the slope and the point on the graph used in creating the equation.
66) y - 1 = 4(x - 7)
66)
67) y + 4 = 6x
67)
12
68) y =
1
(x - 5)
2
69) y = -
68)
1
x
2
Graph the line.
70) y - 1 = -
71) y - 1 =
69)
1
(x - 4)
4
70)
1
(x + 3)
2
71)
Find an equation for the described linear function.
72) Through (0, 1) and parallel to y = -9x - 8
73) Through 0,
72)
7
and perpendicular to 7x - 9y = 3
8
73)
Find an equation in point-slope form of the line having the specified slope and containing the point indicated.
74) m = -4, (-8, 9)
74)
13
75) m =
5
, (-5, 6)
6
75)
Find an equation of the line having the specified slope and containing the indicated point. Write your answer in
slope-intercept form.
76) m = -9; (4, -3)
76)
77) m = 9; (-9, 0)
77)
78) m = 8; (0, -9)
78)
Find an equation of the line containing the given pair of points. Write your final answer as a linear function in
slope-intercept form.
79) (-4, 7) and (-2, 10)
79)
80) (3, -6) and (7, -6)
80)
Solve the problem.
81) The total sales made by a salesperson was $25,000 after 3 months and $68,000 after 23
months. Predict the total sales after 41 months.
82) In 1900 the population of a midwest city was 15,000. By 1910 it had grown to 17,000. If it
continues to grow at the same rate, what will the population be in 1932? Give your answer
to the nearest whole number.
14
81)
82)
Answer Key
Testname: CH3TEST
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
A(-5, 0); B(1, -1)
Quadrant II
None
I and IV
III and IV
I and III
II and IV
No
Yes
Yes
Show that (7, 5) is a solution:
y=x-2
5 =? 7 - 2
5 =? 5
TRUE
Show that (1, -1) is a solution:
y=x-2
-1 =? 1 - 2
-1 =? -1
TRUE
Coordinates of the additional solution may vary but should satisfy y = x - 2.
12) Show that (6, 1) is a solution:
x + 2y
=8
6 + 2(1)
=? 8
=? 8
6+2
8
=? 8
TRUE
Show that (-4, 6) is a solution:
x + 2y = 8
-4 + 2(6)
=? 8
-4 + 12
=? 8
8
TRUE
=? 8
Coordinates of the additional solution may vary but should satisfy x + 2y = 8.
13)
15
Answer Key
Testname: CH3TEST
14)
15) y =
2
x+2
7
16)
17)
18)
19)
20)
21)
22)
y=-x+5
(0, -5), (-7, 0)
(0, 6), (-3, 0), (-2, 0), (1, 0)
(1, 0), (0, 2)
(-2, 0), (0, 2)
(0, 17)
(4, 0)
1
23) 0, - , 2, 0
2
24) (0, 6), (3, 0)
16
Answer Key
Testname: CH3TEST
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
x = -3
y = -1
miles per hour, or miles/hour
bricks per foot, or bricks/foot
$324 per year
$0.92/mi
50 miles per hour
17
Answer Key
Testname: CH3TEST
35)
36)
37) 3 degrees per hour
38) -6 pounds per month
2
39)
3
40) -
3
2
41) Undefined
42) 0
7
43) 8
44) Undefined
45) 0
3
46)
2
47) Undefined
48) 0
18
Answer Key
Testname: CH3TEST
49)
50)
51)
3
; (0, -1)
4
52)
15
; (0, -5)
4
53) 0; (0, 11)
5
54) y = - x + 4
8
55) y = 4x
56)
57) No
58) Yes
59) No
19
Answer Key
Testname: CH3TEST
60) y =
4
x-5
7
61) y = 62) y =
5
5
x+
6
3
3
27
x+
2
2
63) y = -
8
28
x9
9
64)
65)
66)
67)
No
Yes
m = 4; (7, 1)
m = 6; (0, -4)
1
68) m = ; (5, 0)
2
69) m = -
1
; (0, 0)
2
70)
71)
72) y = -9x + 1
9
7
73) y = - x +
7
8
74) y - 9 = -4(x + 8)
20
Answer Key
Testname: CH3TEST
75) y - 6 =
5
(x + 5)
6
76) f(x) = -9x + 33
77) f(x) = 9x + 81
78) f(x) = 8x - 9
3
79) f(x) = x + 13
2
80) f(x) = -6
81) $106,700
82) 21,400
21