Math 90
Exam 3: Study Guide
Section 3.1
Section 3.2
Reading graphs
Graph the following equations by constructing a ta-
1) Use the graph to complete the table.
ble.
x
y
5)
y = 2x
0
6)
2y =
2
7)
y = 2x
8)
x
4
x
1
2y = 2
-4
1
Graph the following equations by using the intercept
The graph in the illustration gives the heart rate of a method.
woman before, during, and after an aerobic workout. Use the 9)
x+y =7
graph to answer the following questions.
10) y = 2x + 5
2)
a. What information does the point ( 10; 60) give us?
11) 3x
b. What was her heart rate one-half hour after beginning the
12) 2x + 3y = 12
2y = 6
workout?
c. At what times was her heart rate 100 beats per minute?
Graph each equation.
13) y =
5
14) 2x = 6
Section 3.3
Determine whether the ordered pair is a solution of
the given system.
(
x+y =2
15) (1; 1) ;
2x y = 1
(
2x 3y = 7
16) (4; 5) ;
4x 5y = 25
Plotting points.
3) Graph each point on the same coordinate grid:
A ( 3; 4) ; B (4; 3:5) ; C
2;
5
2
; D (0; 4) ; E
3
2; 0
Applications
4) The charges for renting a movie are shown in the graph
in the illustration.
a. Find the charge for a 1-day rental.
b. Find the charge for a 2-day rental.
c. Find the charge if the tape is kept for 5 days.
d. Find the charge is the tape is kept for a week.
Solve(each system of equations by graphing.
x+y =2
17)
x y=4
(
3x + 2y = 8
18)
2x 3y = 1
(
3x 6y = 18
19)
x = 2y + 3
(
2x 3y = 18
20)
3x + 2y = 1
(
4x = 3 (4 y)
21)
2y = 4 (3 x)
(
3
4x + y = 3
22)
1
1
4x + y =
Page: 1
Bibiana Lopez
Math 90
Exam 3: Study Guide
Section 3.4
40) An airplane can ‡y downwind a distance of 600 miles
Use substitution
to solve each system.
(
y = 2x + 5
23)
x + 2y = 5
(
b = 2a 9
24)
a + 3b = 8
(
4a + 5b = 2
25)
3a b = 11
(
9x = 3y + 12
26)
4 = 3x y
(
3 (x 1) + 3 = 8 + 2y
27)
2 (x + 1) = 4 + 3y
(
6a = 5 (3 + b + a) a
28)
3 (a b) + 4b = 5 (1 + b)
in 2 hours. However, the return trip against the same wind
takes 3 hours. Find the speed of the wind.
41)
A chemist has one solution that is 40% alcohol and
another that is 55% alcohol. How much of each must she use
to make 15 liters of a solution that is 50% alcohol.
42) A merchant wants to mix the peanuts with the cashews
shown in the illustration to get 48 pounds of mixed nuts to
sell at $4 per pound. How many pounds of each should the
merchant use?
Section 3.5
Section 3.7
Use addition
to solve each system.
(
2x 3y = 11
29)
3x + 3y = 21
(
2x + y = 2
30)
2x 3y = 6
(
3x + 29 = 5y
31)
4y 34 = 3x
(
2x = 3 (y 2)
32)
2 (x + 4) = 3y
(
5 (x 1) = 8 3 (y + 2)
33)
4 (x + 2) 7 = 3 (2 y)
(
4x + 5y = 20
34)
5x 4y = 25
Graph each inequality.
43) y
3 x
44) y < 2
3x
45) 5x + 4y > 20
46) 7x
2y
21
Find the solution set of each system of inequalities,
Section 3.6
Applications
35) One integer is twice another, and their sum is 96. Find
the integers.
when(possible.
x+y < 1
47)
x y> 1
(
2x y < 4
48)
x+y
1
(
x y 5
49)
x + 2y < 4
(
3x + y < 2
50)
y > 3 (1 x)
36) Three times one integer plus another integer is 29. If
the …rst integer plus twice the second is 18, …nd the integers.
37) A plumber wants to cut a 25 foot length pipe into two
pieces so that one piece is 5 feet longer than the other. How
long should each piece be?
Section 8.1
Find the midpoint of the segment joining the given
points.
38) The length of a rectangle is 2 feet more than twice its 51) ( 2; 8) ; (3; 4)
52) (6; 8) ; (12; 16)
width. If its perimeter is 34 feet, …nd its area.
39) A boat can travel 24 miles downstream in 2 hours and 53) ( 3; 5) ; ( 5; 5)
can make the return trip in 3 hours. Find the speed of the
boat in still water.
Page: 2
Bibiana Lopez
Math 90
Exam 3: Study Guide
Section 8.2
Write the equation of the line that passes through
Find the slope of the line that passes through the
the given point and is perpendicular to the given line.
given points.
Write the answer in slope-intercept form.
54) (3; 1) ; ( 6; 2)
73) (2; 5), 4x
55) ( 1; 8) ; (6; 1)
74) (1; 5) ; x =
y=7
3
4y
+5
56) ( 7; 5) ; ( 7; 2)
Determine whether the line P Q is parallel or perpendicular (or neither) to a line with a slope of
2:
57) P (3; 4) ; Q (4; 2)
58) P (5; 4) ; Q (6; 6)
59) P ( 2; 1) ; Q (6; 5)
Section 8.3
Use the point-slope form to write the equation of the
line with the given properties. Write each equation
in standard form (Ax + By = C)
60) m = 5; passing through (0; 7)
61) m =
3; passing through (2; 0)
Use the point-slope form to write the equation of the
line passing through the two given points. Write the
equation in slope-intercept form.
62) P (3; 4) ; Q (0; 3)
63) P (4; 0) ; Q (6; 8)
Use the slope-intercept form to write the equation of
the line with the given properties.
64) m =
7; passing through (7; 5)
65) m = 3; passing through ( 2; 5)
66) Passing through (6; 8) and (2; 10)
67) Passing through ( 4; 5) and (2; 6)
Determine whether the graphs of each pair of equations are parallel, perpendicular, or neither.
68) y = 4x
13; y = 14 x + 13
69) y = 3x + 7; 2y = 6x
70) 2x + 3y = 9; 3x
9
2y = 5
Write the equation of the line that passes through the
given point and is parallel to the given line. Write the
answer in slope-intercept form.
71) (2; 5) ; 4x
y=7
72) (4; 2) ; x = 54 y
2
Page: 3
Bibiana Lopez