Math 060 Review Test 2
Chapter 3 & 4
Chapter 3
1.
2.
3.
Find the slope of the line passing through each given pair of points.
4
3
1
2
a)
( , −2) and (5, )
b)
(−7, 3) and (15, 3)
c)
(𝑎 + 1, 𝑏 − 1) and (2𝑎 − 5, 𝑏 + 5)
d)
(−7, 3) and (−7, 0)
Find the equation of the line passing through the given pair of points. Write your answer in slope-intercept
form if possible.
1 2
3 5
2
3
3
5
a)
(− , ) and ( , − )
b)
(−2, 1) and (−2, −2)
Determine whether the given pair of lines is parallel, perpendicular, or neither.
a) 5𝑥 + 9𝑦 = 27
10𝑦 = 18𝑥 + 50
3
b) 𝑦 = 2 𝑥 − 2
6𝑥 + 4𝑦 = 7
4
c) 𝑦 = 7
7
𝑦 = −4
d) 𝑥 = −2
𝑦 = −2
4.
Find the equation of the line that passes through the point (−9, 7) and is perpendicular to the line 3𝑥 +
5𝑦 = −10. Write your answer in slope-intercept form.
5.
Find the equation of the line that passes through the point (2, −3) and is parallel to the line −5𝑥 + 6𝑦 = 12.
Write your answer in slope-intercept form.
6.
Find the equation of the line that passes through the point (6, 2) and is perpendicular to the line 𝑥 = −4.
1
In problems 7 – 8, state the slope, 𝒙-intercept, and 𝒚-intercept of the given line. Then graph the line on the
given set of coordinate axes.
7.
8.
−4𝑥 + 3𝑦 = −6
Slope: _______ 𝑥-int: _______ 𝑦-int: _______
𝑦−2=0
Slope: _______
𝑥-int: _______ 𝑦-int: _______
y
y
5
5
4
4
3
3
2
2
1
1
x
-5 -4
9.
-3
-2 -1
-1
1
2
3
4
5
x
-5 -4
-3
-2 -1
-1
-2
-2
-3
-3
-4
-4
-5
-5
1
2
3
4
5
The cost to rent a car for a day is $45 plus $0.60 for each mile driven. The total cost, 𝐶, is given by the
equation 𝐶 = 45 + 0.6𝑥, where 𝑥 represents the total number of miles driven.
a)
How much will it cost to drive the car 20 miles?
b)
If you have $75 to spend on renting the car, how far will you be able to drive it?
10. Determine whether each ordered pair is a solution of the system of equations.
2x  5 y  0
x  3 y  11
(a) (3, 1)
(b) (5, 2)
11. Solve the system of equations by graphing. Write the point of intersection as an ordered pair.
y
x  y  1
3x  y  5
5
4
3
2
1
x
-5 -4
-3
-2 -1
-1
-2
-3
-4
-5
1
2
3
4
5
12. Break-even point. Solve the system of equations by graphing.
School Printers, Inc. prints and sells the school newspaper.
The cost y to produce x newspapers is given by the equation y  x  8 .
The revenue y from the sale of these x newspapers is given by the equation y  5 x .
Find the number of newspapers that need to be produced and sold to break-even.____________
y
5
4
3
2
1
x
-5 -4
-3
-2 -1
-1
1
2
3
4
5
-2
-3
-4
-5
In problems 13 – 14, solve the system of equations using substitution. Write the solution
as an ordered pair, or state that there is no solution or infinitely many solutions.
13.
3 x  y  10
x  2y 8
14.
1
3
x
2
4
x  8y  3
y
In problems 15 – 16, Solve the system of equations using elimination. Write the solution as
an ordered pair, or state that there is no solution or infinitely many solutions.
15.
2x  3y  2
5x  7 y  0
16.
4 x  9 y  7
2x  3y   5
17. Solve the system of equations using substitution or elimination. Write the solution as an ordered
pair, or state that there is no solution or infinitely many solutions.
4x  3y  9
4
x  y3
3
18. Solve the system of equations using substitution or elimination. Write the solution as an ordered
pair, or state that there is no solution or infinitely many solutions.
y  5x  3
10 x  2 y  2
19. Solve the system of equations using substitution or elimination. Write the solution as an ordered
pair, or state that there is no solution or infinitely many solutions.
0.25 x  0.10 y  3.70
x
y  25
20. Find two numbers whose sum is
17
1
and whose difference is
.
24
24
21. The measure of one angle is 25 less than the measure of its supplement. Find the measure of
both angles.
22. The sum of twice one number plus second number is fourteen. The first number plus three times
the second number is twenty-two. Find these numbers.
23. Two cities are 400 miles apart. A car leaves one of the cities traveling toward the second city at 45
miles per hour. At the same time, a bus leaves the second city at 35 miles per hour. How long will it
take for them to meet?
24. A jogger leaves a point along a fitness trail running at 5 miles per hour. 20 minutes later, a second
jogger leaves from the same location running at 6 miles per hour. How long will it take the second
jogger to overtake the first?
25. The angle’s measure is 20 degrees more than the triple that of its supplement. Find the angles.
26. Find the measure of the three interior angles of a triangle if the second is 9 degrees more than five
times the first and the third is three times the measure of the first.
27. George is paddling his canoe against the current at 8 mph and with the current at 12 mph. Write a
system of equations that finds George’s paddling speed and the speed of the current.
28. Peanuts sell for $4.00 per pound. Almonds sell for $6.50 per pound. How many pounds of each
type should be mixed together to make a 5-pound mixture that sells for $5 per pound?
29. How many pints of a 25% peroxide solution should be added to 10 pints of a 60% peroxide
solution to obtain a 30% peroxide solution?
Chapter 4
30. Solve and graph the solution set.
3 x
2 
0
3
31. Solve and graph the solution set.
3y
4
 y6
2
32. In order to earn an A in a course, a student must have an average on three examinations of at
least 90. If a student scores 86 and 88 on the first two exams, describe the range of scores that the
student needs on the third test in order to earn an A in the course.
33. Solve each inequality, graph it (if possible), and write the solution set using interval notation.
Identify inequalities that have no solution, or inequalities that are true for all real numbers.
1
a) 3( x  2)  1  1 or  x  3
e)
2 x  4  3  3
2
1
5x  3
4
b) x  1  1 and
f)
 7 x  5  3  3
3
3
c) 4  6  2x  12
g)
2 3x  6  4  8
d) 5 1  2 x  6  9
h)
1
 x  1  4  2
2
34. Solve each equation. Identify equations that have no solution, or equations that are true for all
real numbers.
a)
2 x  4  20  10
d)
5x  3  5x  1
b)
2  3x  12  2
e)
2x 1  x  3
c)
3  2x  3  6
f)
2x 1  2 x 1