Download MTH Week 8 Checkpoint Assignment -- Due Day 3

MTH 157
Week 8 Checkpoint Assignment
Due Day 3--- Wednesday
Name:
-1-
Score:
MTH Week 8 Checkpoint Assignment -- Due Day 3 (Wednesday)
Instructions: In order to complete your checkpoint in an organized and efficient manner,
please use this template to type your work and answers.



Use the Equation Editor in Microsoft® Word to show your work.
Copy and paste charts and graphs from Microsoft® Excel® into Microsoft® Word.
Submit the Microsoft® Word document as an attachment in your individual forum.
Problem
Section 13.3 pp.
826-828
#6
Type your solution here
The graph of y = -4x + 5 is shown on the next page. Use it to
find the answers to Exercises 6–8. Check your work.
6. The value of y when x = 1
Work:
if x=1  y=-4(1)+5=-4+5=1
Answer: y = 1
Section 13.3 pp. 826828
#8
The graph of y = -4x + 5 is shown on the next page. Use it to find
the answers to Exercises 6–8. Check your work.
8. The value of x when y = -3
Work:
if y=-3  3=-4x+5
-4x=-5-3=-8
x=-8/-4=2
Section 13.3 pp. 826828
# 12
Answer: x = 2
Without graphing, identify the slope and the y-intercept for the line
associated with each equation or table of values in Exercises 9–15.
12.
5x + 20y = 60
Work:
5 x  20 y  60
20 y  5 x  60
5
60
1
y  x
  x3
20
20
4
Answer: slope = -1/4
Section 13.3 pp. 826828
# 26
26. Use two points on any horizontal line to illustrate why a
horizontal line has a slope of 0.
Let the equation y=3 (horizontal line)
2 points on the line are: (1,3) and (3,3)
Please leave this column
blank.
MTH 157
Week 8 Checkpoint Assignment
33 0
 0
Then slope =
3 1 2
Section 13.3 pp. 826828
# 28
Due Day 3--- Wednesday
28. The equation y = 12x + 5 shows the total cost for ordering tickets
on the phone for a certain outdoor concert. Tickets are $12 each, and
there is a one-time service
fee of $5. Can the slope of this line be thought of as a rate? Explain.
Answer: Yes,slope of the line is 12 and is the cost per ticket
Section 13.3 pp. 826828
# 32
Write an equation that satisfies the conditions stated in Exercises 31–
35.
32. Parallel to the line y = -4x + 1
Work:
Slope is -4 so any line with slope -4 is parallel
Section 13.3 pp. 826828
# 36
Answer: y=-4x+5
What happens to the value obtained for the slope if
the coordinate of the two ordered pairs aren´t
substracted in the same order? Give an example as
part of your explanation.
Example: points: A  (2, 4), B  (2,1)
1 4
3 3


Slope =
2  2 4 4
If we change the order:
Slope=
4 1
3
3


2  2  4
4
Answer:slope changes the sign
Section 13.3 pp. 826828
# 40
40. The Egg Problem. A certain zoo kept records of the relationship
between the weight of a mother ostrich and the weight of her egg.
Data for three birds is shown in
the next table.
a. Estimate the weight of an egg from a mother ostrich weighing 175
lbs.
slope =
3.2  2.4 0.8

 0.02
160  120 40
-2-
MTH 157
Week 8 Checkpoint Assignment
Due Day 3--- Wednesday
y  0.02 x  b and (120,2.4)is in the line
 2.4=0.02(120)+b
2.4=2.4+b  b=0
 Line: y=0.02x
Work:
if x=175  y=0.02(175)=3.5
Answer: 3.5 lbs
b. How much would you expect the egg to weigh from a mother
ostrich weighing 190 lbs?
if x=190  y=0.02(190)=3.8
Answer: 3.8 lbs
Section 13.4 pp.
847-850
#4
In Exercises 2–5, find the midpoint of the line segment having the
given endpoints.
(8, 1) and (2, 9)
Work:
midpoint is:
 8  2 1 9 
,

  (5,5)
2 
 2
Answer: midpoint is (5,5)
Section 13.4 pp. 847850
#8
In Exercises 6–9, find the other endpoint of a line segment with the
given midpoint and one endpoint.
8. Endpoint (0, 0); midpoint ( 4, -3)
Let the other endpoint =P=(x,y)
 x0 y0
,

  (4, 3)
2 
 2
x0
y0
 4,
 3
2
2
x  8, y  6
Section 13.4 pp. 847850
# 14
Answer: (8,-6)
Find the distance between the given points in Exercises 11–14.
( -3, -7) and ( -4, 15)
D=
d  (4  3) 2  (15  7) 2  485  22.02(approx)
Answer: 22.02
-3-
MTH 157
Week 8 Checkpoint Assignment
Due Day 3--- Wednesday
Find
the
equations
of
the
lines
shown
in Exercises 27–29 by using the
Section 13.4 pp. 847slope-intercept method. Be sure to check the scale of the graph.
850
# 28
60 6
3


Slope =
0  8 8
4
y-intercept is 6
Answer:
y 
3
x6
4
Section 13.4 pp. 847850
# 30
1st line: passing through (0,2) and (-3,-2)
Slope is:
2  2 4 4
4

  y  xb
3  0 3 3
3
Using: (0,2)
4
4
2= (0)  b  b  2  y  x  2
3
3
2nd line: passing through (0,-1) and (-2,1)
Slope is:
1  (1) 2

 1  y   x  b
2  0 2
Using: (0,-1)
-1=  (0)  b  b  1  y   x  1
We have to solve:
-4-
MTH 157
Week 8 Checkpoint Assignment
4

y  x  2
3

 y   x  1
Due Day 3--- Wednesday
4
x  2  x 1
3
4 
  1  x  1  2
3 
7
x  3
3
9
9
2
x    y  1 
7
7
7
Answer: (-9/7,2/7)
Section 13.4 pp. 847850
# 32
Give the equation of the circle with the given center and radius in
Exercises 31–34.
Center at (1, 2); radius = ½
Work:
1
( x  1)  ( y  2)   
2
1
( x  1) 2  ( y  2) 2 
4
2
2
2
Answer: ( x  1) 2  ( y  2) 2 
Section 13.4 pp. 847850
# 42
1
4
Sketch the line x = 6. How is it related to the line y = 6?
Answer: x=6 is a vertical line and y=6 is a
horizontal line so both lines are perpendicular
Section 13.4 pp. 847850
# 50
Garden Area Problem. A designer created a garden from two
concentric circles whose equations are as follows:
(x + 2)² + ( y - 6)² = 16
And
(x + 2)² + ( y - 6)² = 81.
-5-
MTH 157
Week 8 Checkpoint Assignment
Due Day 3--- Wednesday
The area between the circles will be covered with grass. What is the
area of that section?
Work: radius of the first circle is 16=4 and radius of the second
circle is 81=9
Area of the greatest circle is 81pi and area of the smallest circle is
16pi so area of the section is (81-16)pi =65pi
Answer:Area is 65pi square units
Section 13.4 pp. 847850
# 52
Taxicab Distances Problem. Imagine that the grid lines on a
coordinate grid are streets and that the distance between two points
must be measured by the number of “blocks” a taxicab would have to
travel horizontally and vertically to get from one point to the other.
The sum of the horizontal and vertical distances is called the taxicab
distance. A cab driver estimates that traveling one block during rush
hour takes about 5 min. Use this information to answer Exercises 51
and 52.
How do you find the distance between two points?
Work: distance = (8-2)+(8-1)=6+7=13
Answer: 13
General rule:
A=(xa,ya); B=(xb,yb)
Distance = |yb-ya|+|xb-xa|
Answer:d = |yb-ya|+|xb-xa|
Section 13.4 pp. 847850
# 54
54. Suppose that someone said that the equation connecting
points ( -1, 1) and ( 2, 3) is
y
2
5
x .
3
3
This person
wants to know whether the line represented by this
equation will contain point (6, 9). Identify two ways by which this
person can decide whether the graph of the equation contains the
point.
Work:
-6-
MTH 157
Week 8 Checkpoint Assignment
Due Day 3--- Wednesday
1st way:
If x = 6 then y = (2/3)6+5/3=4+5/3=17/3≠9
Then (6,9) is not in the line
y
2
5
x
3
3
2nd way:
Slope of the line determined by (-1,1) and (6,9) is
(9-1)/(6+1)=8/7 ≠2/3
Then (6,9) is not in the line
CH. 13 Review
pp. 852-853
#2
y
2
5
x
3
3
Tell whether each quantity in Exercises 1 and 2 is constant or
variable. Explain.
2. The number of hours in a day
Constant because every day has 24 hs
CH. 13 Review pp.
852-853
#6
For Exercises 5–7, the total cost of hiring a certain plumber is a flat
rate of $35 plus $9.50/hr.
6. Write an equation that shows the relationship between
the quantities.
X=number of hours
Y=total cost
Y=9.5x+35
CH. 13 Review pp.
852-853
#10
Solve each equation in Exercises 10 and 11 by using the properties of
equality. Check.
10. 4x – 18 = 65
4x=65+18
4x=83
X=83/4
Answer: x=83/4
CH. 13 Review pp.
852-853
# 14
-7-
MTH 157
Week 8 Checkpoint Assignment
Due Day 3--- Wednesday
Answer: -5,3
CH. 13 Review pp.
852-853
# 18
Find the slope of the line passing through
points ( 3, 11) and ( 18, 20)
slope =
CH. 13 Review pp.
852-853
# 22
CH. 13 Review pp.
852-853
# 26
CH. 13 Review pp.
852-853
# 30
20  11 9 3
 
18  3 15 5
Answer: 3/5
.
Find the distance between the given points in Exercises 21 and 22. (
-5, 5) and ( 0, 12).
d  (12  5) 2  (0  5) 2  74  8.6( approx)
Answer: 8.6
Give the equation of a line that is parallel to y = -4x + 7.
That line must have the same slope (-4)
Answer: y= -4x+1
The graph of an equation in the form y = mx + b is a
straight line. Can the equation of every straight line be
written in the form y = mx + b ? (Hint: What is the
equation of a vertical line?)
Answer: No, x=a is a vertical line
CH. 13 Review pp.
852-853
# 34
Give an equation of a line perpendicular to the line y = 4x
having the same y-intercept.
Slope of y=4x is 4 then 4m=-1
where m is the slope of the line required
m = -1/4
then y = (-1/4)x+b
y-intercept of y=4x=0
then b=0
Answer: y = (-1/4)x
CH. 13 Review pp.
852-853 # 38
OMIT 
WEEKLY QUESTION:
-8-
MTH 157
Week 8 Checkpoint Assignment
Due Day 3--- Wednesday
-9Review the NCTM Principles and Standards Web site at http://standards.nctm.org/document/index.htm
Include your response to the following question with your CheckPoint:
What are two standards that relate to the content addressed this week?
Discuss the ways in which this series of problems meets the standards.