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Math 025
Weekly Homework #4
1. Complete the table of
values. Write the results as
ordered pairs.
2x + 3y = 12
x
y
0
0
8
2. What is the slope of a
line whose graph is
parallel to the graph of
3x + y = 7? Perpendicular
to the graph of 3x + y = 7?
3. Use the indicated points
to find the slope of the line.
p. 202: 40
4. Write the expression by
using exponents.
p. 229: 53
5. Use the product rule, if
possible, to simply the
expression.
 1  1  1  1  1 
          
 4  4  4  4  4 
58 ∙ 39
p. 227: 5
6. Use the power rules for
exponents to simplify the
expression. Write the
answer in exponential
form.
(t4)5
p. 261: 8
7. Graph the linear equation 3x + y = -6.
p. 262: 41
8. For each equation, give
the slopes of the lines and
then determine if the two
lines are parallel,
perpendicular, or neither.
p. 262: 45
9. Find the slope of the
line through the points
(0, 3) and (-2, 0).
5x – y = 1
x – 5y = -10
p. 215: 38
p. 229: 63
p. 229: 29
10. Match each equation with the graph that would most closely resemble its graph.
a)
b)
c)
d)
y=x+3
y = -x + 3
y=x–3
y = -x – 3
A.
C.
p. 239: 5
11. It costs $400 to start up a business selling snow cones.
Each snow cone costs $0.25 to produce.
a) What is the fixed cost?
b) What is the variable cost?
c) Write the cost equation.
d) What will be the cost of producing 100 snow cones,
based on the cost equation?
e) How many snow cones will be produced if the total cost
is $775?
B.
D.
12. The ordered pair (3, 2)
is a solution to the equation
2x – 5y = ________
p. 201: 10
p. 241: 67
13. Explain why the equation
of a vertical line cannot be
written in the form
y = mx + b.
14. Use the product rule,
if possible, to simply the
expression.
(-6p5)(-7p5)
15. Assume that a is a
number greater than 1.
Arrange the following
terms in order from least to
greatest:
-(-a)3, -a3, (-a)4, -a4
p. 239: 6
p. 262: 35
p. 263: 89
16. Find the x-intercept and
the y-intercept for the graph
of the equation
2x – 3y = 24.
17. Write the equation of
the line with an undefined
slope and a y-intercept of
(0,5).
18. Simplify the
expression.
p. 215: 17
19. Simplify by writing the
expression with positive
exponents. Assume that all
variables represent nonzero
real numbers.
p. 240: 16
20. Use the product rule,
if possible, to simply the
expression.
38 + 39
p. 262: 76
21. Simplify by writing
the expression with
positive exponents.
Assume that all variables
represent nonzero real
numbers.
(3x4y2z)3(yz4)5
p5q-8
 xy  2
 2
 x y
p. 270: 43
p. 262: 39
22. If a line is vertical, what
is true of any line that is
perpendicular to it?
23. Write the equation of
the line perpendicular to
x – 2y = 7 with a yintercept of (0, -3).



3
p. 271: 71
24. Simplify by writing
the expression with
positive exponents.
Assume that all variables
represent nonzero real
numbers.
( x 1 y 2 z ) 2
( x 3 y 3 z ) 1
p. 229: 56
p. 241: 65
p. 271: 69
25. Graph the line passing
through the point (-1, 4) with
the slope 2/5.
26. Write the equation of
the line with a slope of 0
and a y-intercept of (0,3).
27. Write the equation of
the line through (2, -3)
parallel to 3x = 4y + 5.
p. 240: 29
28. Find the slope of the line
through the points
(-4, -5) and (-5, -8).
p. 240: 13
29. Is the ordered pair
(0, 9) a solution of the
equation x + y = 9?
p. 229: 32
p. 202: 16
p. 241: 63
30. It costs a flat fee of
$20 plus $5 per day to rent
a pressure washer.
Therefore, the cost to rent
the pressure washer for x
days is given by
y = 5x + 20, where y is in
dollars. Express each of
the following as an ordered
pair:
a) When the washer is
rented for 5 days, the cost
is $45.
b) I paid $50 when I
returned the washer, so I
must have rented it for 6
days.
31. Evaluate the expression.
32. Simplify the
expression.
(-4)-3
 6x3 y 9

5
 z
p. 204: 73
33. Use the product rule, if
possible, to simply the
expression.
4

 (z ≠ 0)

t3 ∙ t8 ∙ t13
p. 262: 31
p. 270: 24
p. 262: 80
34. The weight y (in pounds) of a man taller than 60 in.
can be approximated by the linear equation y = 3.9x + 73.5,
where x is the height of the man in inches.
a) Use the equation to approximate the weights of men
whose heights are 62 in., 66 in., and 72 in.
b) Graph the equation, using the data in a)
c) Use this graph to estimate the height of a man who
weighs 155 lb. Then use the equation to find the height of
the man to the nearest inch. (Hint: Substitute for y in the
equation.)
35. Write an equation for
each line passing through
(-2, 5) and having the slope
2/3.
p. 240: 39
36. Complete the ordered
pair for the equation
y = -4x + -4.
(
, 24)
p. 202: 37
p. 216: 63
37. For each equation, give
the slopes of the lines and
then determine if the two
lines are parallel,
perpendicular, or neither.
38. Graph the linear
equation y = -6x.
39. Is the ordered pair
(4, 2) a solution of the
equation x – 6 = 0?
2x + 5y = 4
4x + 10y = 1
p. 202: 27
p. 229: 57
p. 215: 47
40. Find the slope of the line
y = 2x – 3.
41. Decide whether the
slope is positive, negative
or zero, and whether the yvalue of the y-intercept is
positive, negative, or zero.
42. Complete the table of
values and then plot
ordered pairs.
3x – 4y = 12
x
y
0
0
-4
-4
p. 228: 19
44. Simplify by writing
the expression with
positive exponents.
Assume that all variables
represent nonzero real
numbers.
p. 203: 67
45. Find an expression that
represents the area of the
figure.
p. 229: 40
43. Find the slope of the line
through the points
2 1
1 5
 ,  and  ,  .
3 2
3 6
6a3
(7 4 ) 3
79
p. 229: 38
p. 271: 57
46. Complete the ordered
pair for the equation
y = 2x + 7.
47. For the equation
y = mx + b, what is the yvalue corresponding to x =
0 for any value of m?
(
p. 263: 86
48. Evaluate the
expression.
5-1 + 3-1
, -3)
p. 202: 33
p. 202: 39
p. 270: 25
49. Use the power rules for
exponents to simplify the
expression. Write the answer
in exponential form.
(-52)6
50. Use the equation
3x = -y – 6 to complete the
given ordered pairs. Then
graph the equation by
plotting the points and
drawing a line through
them.
51. Is the ordered pair
(5, 2) a solution of the
equation 5x – 3y = 15?
p. 202: 21
p. 262: 51
52. What is the equation of
the x-axis? What is the
equation of the y-axis?
(0, ), ( , 0),
 1

 , 
 3

p. 214: 5
53. Graph the equation by
using the slope and yintercept.
1
y  x4
3
p. 215: 31
55. Graph the linear equation
x + 2= 8.
54. Write the equation of
the line with a slope of -5
and a y-intercept of (0,6).
p. 240: 12
p. 240: 19
56. Evaluate the
expression.
70 + 90
p. 270: 15
57. Use the power rules for
exponents to simplify the
expression. Write the
answer in exponential
form.
1
 
2
3
p. 262: 59
p. 215: 55
58. Complete the table of
values. Write the results as
ordered pairs.
x = -9
x
y
6
2
-3
59. Use the geometric
interpretation of the slope
to find the slope of the
line. Then, by identifying
the y-intercept from the
graph, write the slopeintercept form of the
equation of the line.
p. 202: 44
60. Simplify by writing
the expression with
positive exponents.
Assume that all variables
represent nonzero real
numbers.
(4a 2 b 3 ) 2 (2ab 1 ) 3
( a 3 b)  4
p. 271: 73
61. Find the slope of the line
x = 6.
p. 239: 9
62. The ordered pair
(_____, -2) is a solution of
the equation x = 6.
p. 229: 51
64. The ordered pair
(4, _____) is a solution of the
equation y = 3.
p. 201: 14
65. Do (4, -1) and (-1, 4)
represent the same ordered
pair? Explain.
p. 202: 19
66. Find the slope of the
line y = 2x – 3.
p. 201: 13
67. Graph the linear equation
x – 1 = -4.
p. 202: 28
68. Simplify by writing
the expression with
positive exponents.
Assume that all variables
represent nonzero real
numbers.
p. 229: 43
69. Write an equation for
the line passing through the
points (-2, -1) and (3, -4).
63. Is the ordered pair
(3, –1) a solution of the
equation 2x + y = 5?
3 2
5 3
p. 215: 56
p. 270: 31
p. 241: 49
70. A ski slope drops 25 feet vertically for every 100 horizontal feet. Which of the
following express its slope? (Hint: There is more than one correct answer.)
A. 
1
4
B. -4
C. 
25
100
-25 ft
D. -0.25 E. -25 F. -25%
100 ft
p. 228: 24
Things you should know:
Point
Ordered Pair
Origin
x-intercept
y-intercept
Slope
Vertical slope
Horizontal slope
Linear Equation
Standard form of the equation of the line
Slope-intercept form of the equation of the line
Point-slope form of the equation of the line
Parallel
Perpendicular
Product Rule for exponents
Power rules for exponents
Zero exponent
Negative exponent
Quotient rule for exponents