Name Unit 1 Post-Testpaulcamaren.wikispaces.com/file/view/SPP.Linear Equati… · Web view2018-03-14 · How many weeks will you have to save up your allowance in order to buy the

Linear Equations WS#1a Parallel and Perpendicular Activity Name ______________________________Grade: _______

1. The following equations are graphed to the right. Line A: y = 3x + 2

Line B: y = 3x + 4

Label each graph line A or B

a) What is the slope of Line A? What is the y-intercept?mA=¿ y−∫ .A=¿ y A=¿

b) What is the slope of Line B? What is the y-intercept?mB=¿ y−∫ .B=¿ yB=¿

c) What do you notice about the lines?

2. Graph and label the following 3 equations on the graph to the right, by first plotting all integer coordinates, then making theline for each.

a) y = x + 4 b) y = x c) y = x – 4

3. What is the name used to describe these lines? Where will these lines intersect?

4. Do all the lines have the same slope? Do they have the same y-int.?ma=¿ mb=¿ mc=¿

ya=¿ yb=¿ yc=¿y−∫ .a=¿ y−∫ .b=¿ y−∫ .c=¿

5. Can you make any connection about the lines, their slopes and y-int.? q r s

6. Use the graph to the right to answer the following questions:

a) Find the slopes and y-int. for each line.mq=¿ mr=¿ ms=¿

y−∫ .q=¿ y−∫ .r=¿ y−∫ .s=¿

yq=¿ yr=¿ ys=¿

b) Are these three lines parallel?

c) Are linear equations that have the same slope always parallel?

7. Write the equations of any three lines that are parallel.a) ya=¿

b) yb=¿

c) yc=¿

Linear Equations WS#1b Parallel and Perpendicular Activity Name ________________________Grade: _____

1. The following equations are graphed to the right.Line A: y = -3x + 5 (Label line A on the graph)

Line B: y=13x (Label line B on the graph)

a) What is the slope of Line A? What is the equation?mA=¿ ya=¿

b) What is the slope of Line B? What is the equation?mB=¿ yb=¿

c) What do you notice about the angle where these two lines intersect? What is the term used to describe this?

2. Graph each set of equations below. First plot all integer coordinates, then make the line for each. Label lines.

a) y1=2 x+3

y2=−12x+3 b)

y1=32x+2

y2=−23 x−4

c) y1=x−2y2=−x+7

3. Indicate the ≈ solution ______ ≈ ______ ≈ ______

4. What do you notice about the angle that each set of lines intersect at? How are these lines called?mA1=¿ mA2=¿ mB1=¿ mB2=¿ mC 1=¿ mC 2=¿

5. What do you notice about each pair of slopes?

6. What conjecture can you make about slopes of perpendicular lines? (Similar answer to #12)

7. Perpendicular lines have slopes that are opposite reciprocals of each other. Find the perpendicular slopes of the following given slopes:

a) ma=5 b) mb=−14 c) mc=−3 d) md=

32 e) me=1

ma⊥=¿ mb⊥=¿ mc⊥=¿ md⊥=¿ me⊥=¿

8. Write the equation of any two sets of lines that are perpendicular to each other.a) ya=¿

b)ya⊥=¿

* Perpendicular Lines can also be when one slope is undefined (dividing by 0 in undefined) and the other slope = 0 (0 divided by a number).Linear Equations WS#2 (Three Forms) Name ______________________

1) Line A contains the points (3, -1) and (-1, 2). Line B graphed in the same coordinate plane contains the points (2, 0) and (-2, 3). Could these lines be either parallel or perpendicular? Explain.

2) Line C contains the points (0, -2) and (1, 3). Line D graphed in the same coordinate plane contains the points (3, -1) and (-2, 0). How do these two lines relate to each other? Explain.

3) Line E contains the points (0, -1) and (-1, 2). Line F graphed in the same coordinate plane contains the points (2, 0) and (-2, 3). How do these two lines relate to each other? Explain.

--------------------------------------------------------------4) Write the equation of a line in slope-intercept form:

(a) parallel and (b) perpendicular to the line: 4x - 2y = 8 and contains the point (-6, 2).

5) Write the equation of a line in slope-intercept form: (a) parallel and (b) perpendicular to the line:3x - y = - 2 and contains the point (1, 3).

6) Write the equation of a line in slope-intercept form: (a) parallel and (b) perpendicular to the line:2x + 3y = 9 and contains the point (6, 4).

7) Write the equation of a line in slope-intercept form: (a) parallel and (b) perpendicular to the line:2y - x = - 2 and contains the point (-4, 3).

--------------------------------------------------------------8) Write the equation of a line in all three forms

which contain the points (-4, 6) and (8, 12)

9) Write the equation of a line in all three forms which contain the points (3, 6) and (12, 24)

10) Write the equation of a line in all three forms which contain the points (2, 1) and (-3, -9)

11) Write the equation of a line in all three forms which contain the points (3, 7) and (-5, -9)

12) Write the equation of a line in all three forms which contain the points (-3, -5) and (6, -2)

13) Write the equation of a line in all three forms which contain the points (-2, 1) and (2, 9)

Linear Equations WS#3 (Three Forms) Name ______________________

Know both line with an undefined slope and line with a slope = 0

1) Line A contains the points (-2, -1) and (7, 5). Line B graphed in the same coordinate plane contains the points (7, -3) and (-1, 9). How do these two lines relate to each other? Explain.

2) Line C contains the points (-3, -2) and (-3, 10). Line D graphed in the same coordinate plane contains the points (-4, 7) and (3, 7). How do these two lines relate to each other?

3) Line E contains the points (-10, -8) and (-4, -6). Line F graphed in the same coordinate plane contains the points (4, 2) and (10, 4). Could these lines be either parallel or perpendicular? Explain.

------------------------------------------------------------4) Write the equation of a line in slope-intercept form:

(a) parallel and (b) perpendicular to the line: 5x + 3y = 23 and contains the point (-15, 6).

5) Write the equation of a line in slope-intercept form: (a) parallel and (b) perpendicular to the line:2x + y = 8 and contains the point (8, -7).

6) Write the equation of a line: (a) parallel and (b) perpendicular to the line: x = 7 and contains the point (2, -4).

7) Write the equation of a line: (a) parallel and (b) perpendicular to the line: y = 3 and contains the point (-3, 7).

---------------------------------------------------------8) Write the equation of a line in all three forms

which contain the points (5, 4) and (10, 7)

9) Write the equation of a line in all three forms which contain the points (-4, 6) and (8, 12)

10) Write the equation of a line in all three forms which contain the points (-1, -3) and (1, -1)

11) Write the equation of a line in all three forms which contain the points (-9, 2) and (-8, 6)

12) Write the equation of a line in all three forms which contain the points (-3, 1) and (-6, 3)

13) Write the equation of a line in all three forms which contain the points (2, 3) and (1, -4)

14) Write the equation of a line in all three forms which contain the points (3, 4) and (6, -5)

Linear Equations WS#4 (Three Forms) Name ______________________ 1. Define slop e:: m = Δy /Δx Check using table: Pos = / & Neg = \2. Three Linear Forms:

MPS: y = m(x - h) + k Use 1st ordered pair furthest to left

SI: y = mx + b Check equation using last slope in y-intercept

SF: Ax + By = C Check answer using last ordered pair on right

For all graphs make a table to find all ordered pairs. Next find slope mathematically. Next write the equation of the graph in all three forms: MPS, SI and SF (Modified Point Slope, Slope-Intercept and Standard Format). Do checks.1) What are the linear equation of the scatter plot?

2) State the linear equations for the following graph.





7) What do you notice about the values of h & k in the MPS equation?

Linear Equations WS#5 (Three Forms) Name ______________________ Know both line with an undefined slope and line with a slope = 0

1) Find the slope between points: (Not three forms)(-1, 4) and (5, 9)

2) Find the slope between points: (Not three forms)(3, 5) and (0, 4)

3) What is the slope between points (0, 5) and (0, 9)? (Not three forms)

For all graphs make a table to find all ordered pairs. Next find slope mathematically. Next write the equation of the graph in all three forms: MPS, SI and SF (Modified Point Slope, Slope-Intercept and Standard Format). Do Checks.






9) Write the equation for a line in all three forms for a line with a slope of -2 that passes through (-1, 3).

10) Write the equation for a line in all three forms for a line that passes through (0, -2) and (3, 4).

11) Write the equation for a line in all three forms for a line that passes through (-4, 5) and (4, 1).


For each of the following write the equation in all three forms: MPS, SI and SF (Modified Point Slope, Slope-Intercept and Standard Format). Do Checks.1) Write the equation for a line in all three forms for a

line that passes through (1, 3) and (2, 5)

2) Write the equation for a line in all three forms for a line that passes through (2, 2) and (6, 0)

3) Write the equation for a line in all three forms for a line that passes through (-1, 3) and (1, -1)

4) Write the equation for a line in all three forms for a line that passes through (-3, -6) and (-1, -2)

5) Write the equation for a line in all three forms for a line that passes through (-6, -6) and (-3, -5)

6) Write the equation for a line in all three forms for a line that passes through (-1, 6) and (1, -4)

7) Write the equation for a line in all three forms for a line that passes through (0, -3) and (2, -5)

8) Write the equation for a line in all three forms for a line that passes through (1, 5) and (-1, -5)

9) Write the equation for a line in all three forms for a line that passes through the following y-coordinates. Find the 4th, 5th, 6th terms in the pattern. Use SI to find the 100th term. 0, 5, 10, ___, ___, ___

10) Write the equation for a line in all three forms for a line that passes through the following y-coordinates. Find the 5th, 6th ,7th terms in the pattern. Use SI to find the 100th term. -1.5, 0, 1.5, 3, ___, ___, ___

11) Write the equation for a line in all three forms for a line that passes through the following y-coordinates. Find the 5th, 6th, 7th in the pattern: Use SI to find the 100th term. 5, 5.5, 6, 6.5, ___, ___, ___

12) Write the following in SI and solve. Suppose you receive $11 every week in allowance from your parents. If you do not spend any of your allowance for 9 months, how much money will you have saved? (Assume each month = 4 wk). Try this problem again using Dimensional Analysis.

13) Write the following in SI and solve. Suppose you receive $12.50 every week in allowance from your parents. You want to purchase a video game that costs $150. How many weeks will you have to save up your allowance in order to buy the video game? Try this problem again using Dimensional Analysis.


1) Given the following table, write the equation in MPS and SI forms for a line that passes through the following coordinates. Use SI form to find the 100th value (y). Do Mental Check.

Term Number (x) Term Value (y)1 2.52 4.53 6.54 8.5


Term Number (x) Term Value (y)1 2.52 33 3.54 4


Term Number (x) Term Value (y)1 62 113 164 21


5) Given the following SI equation: y = 1/3 x + 3 find the value of the 99th term.

6) Given the following SI equation: y = 2x – 4 find the value of the 50th term.

Linear Equations WS#8 (Three Forms) Name: ______________________________ Grade: ____ Date: ______

Celsius, also known as centigrade, is a scale and unit of measurement for temperature. It is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale. The degree Celsius (°C) can refer to a specific temperature on the Celsius scale as well as a unit to indicate a temperature interval, a difference between two temperatures. The unit was known until 1948 as "centigrade" from the Latin centum translated as 100 and gradus translated as "steps".

From 1743 until 1954, 0 °C was defined as the freezing point of water and 100 °C was defined as the boiling point of water. (Although these defining correlations are commonly taught in schools today, by international agreement the unit "degree Celsius" and the Celsius scale are currently defined by two different temperatures: absolute zero, and the triple point of purified water).

Fahrenheit (symbol °F) is a temperature scale based on one proposed in 1724 by the physicist Daniel Gabriel Fahrenheit (1686–1736), after whom the scale is named. The scale is defined by two fixed points: the temperature at which water freezes into ice is defined as 32 degrees, and the boiling point of water is defined to be 212 degrees.

By the end of the 20th century, most countries used the Celsius scale rather than the Fahrenheit scale. Fahrenheit remains the official scale for the following countries: Jamaica, the Cayman Islands, Belize, the Bahamas, and the United States of America and associated territories.

Given the thermometers scales shown below, find a mathematical relationship between the two systems.

1. Most adults (especially here in Colorado) know that water freezes at 0 °C , which in Fahrenheit equals 32°F. According to the picture on the right, what temperature in °F would 10 °C ° be?

2. What does the x (independent variable) and y (dependent variable) refer to in your “table”?

3. Using the question and answer from above, find the slope that relates these two temperature systems.

4. Using the slope and one of the coordinates used in question 1, find the equation in Modified Point Slope Format that relates these two temperature systems.

5. Write the equation in Slope-Intercept Form that relates these two temperature systems.

6. Using your SI equation find the exact corresponding temperature to 20°C? Compare your answer to the given thermometer picture. Do you think you are correct – Explain.

7. Using your SI equation find the exact corresponding temperature to 86°F? Compare your answer to the given thermometer picture. Do you think you are correct – Explain.

8. Make a table with 15 equivalent temperatures. Compare your answer to the given thermometer picture. Do you think you are correct

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=W5kj4b4364wswM&tbnid=6tjrmhItqwG5bM:&ved=0CAUQjRw&url=http://www.oocities.org/stjoegrade6/tools.html&ei=h8dFUouJD4i0rQHxq4GIDg&bvm=bv.53217764,d.aWM&psig=AFQjCNGK0YpF8ScQmDoYH8CsBJO-FFY2dA&ust=1380391004722311


For each of the following describe in words what the slope means as well as any coordinates. Next write the equation of the line for each problem below in ALL three forms. Perform a check if given more than one coordinate. Use SI to solve unknowns.

1) A city mouse gains five cheese crumbs for every person it scares. After it has scared 3 people it had 27 cheese crumbs. a) How many cheese crumbs will this city

mouse gain if it has scared 25 people?b) How many people did this city mouse scare

if it has gained 57 cheese crumbs?

2) Christopher currently has $300 in his savings account. Each month he deposits $20.a) How much money will Christopher have if

he saves for 18 months?b) How long will he have to save in order to

have $1020?

3) After 12 months of saving, Luke has saved $200. Each month he deposits $15. a) How long will he have to save in order to

buy a $500 bike?b) How much money will Luke have after

saving for 11 months?

4) The first week Sofia sold 23 tickets to a game and collected $115. The next week she sold 18 tickets to the same game and collected $90. a) If the total collected was $600, how many

tickets were sold?b) If only 15 tickets could be sold how much

money would be collected?

5) Lucia babysat her cousins for 4 hours and was paid $28. The next weekend she babysat another cousin for 12 hours and earned $84.a) How much money will Lucia have if she

babysits her cousins for 9 hours?b) How many hours will she have to babysit in

order to buy a $147 pair of designer jeans?

6) A washing machine repair shop charges $60 per hour plus a house call service fee of $90.a) If the job total collected was $330, how

many hours were worked?b) If a job required 7 hours of work how much

money would be collected?

7) Mateusz is a parachutist at an altitude of 3000 ft. and descending 25 feet every second. a) If the ground is at an altitude of 250 feet,

how long will he have in the air before landing?

b) What height will he be after 30 seconds?

8) When a plumber comes out to the house, the charge is $70 per hour plus a house call service fee of $80.a) If a job required 5 hours of work how much

money would be owed?b) If the job total collected was $290, how

many hours were worked?

9) Logan has been saving $15 each week. After 7 weeks of savings, he has $215 in his account.a) How much money did Logan have before

he started saving? What is this point called?b) How long will he have to save in order to

buy a $300 game?

10) Carina sold 7 tickets to a concert and collected $42. The next week she sold 9 tickets to the same concert and collected $54. a) If Carina sold a total of 18 tickets, how

much money would she have collected?b) If sales from the concert totaled $750, how

many tickets were sold?

Linear Equations WS#10 (Word Problems) Name ______________________

1) Noah uses this formula to calculate the monthly profit of his bicycle store: P = 400n – 7200. In the formula, P is the monthly profit and n is the number of bicycles sold in a month. How many bicycles must he sell to make a profit of exactly $2,000 in a month?

2) Use the indicated temperatures in the above thermometer to calculate slope. Explain what the slope means in words. Next write an equation in both MPS and SI form. a) What equivalent temperature is -30o C?b) What equivalent temperature is 455o F?

For each of the following questions make a data table of at least 3 values to help you find the equation that represents each of the following situations. Solve using either MPS or SI. Check mentally.

3) Bowling cost $3 for the first game and each additional game cost $2. (a) If a person wants to play 10 games how much will it cost? (b) If a person has $13, how many games can be played?

4) Each month, Kylee’s phone company charges her $10 for the first 3 minutes of phone calls and $0.25 for each additional minute. What is the cost for 12 minutes?

5) Marcus is kayaking in a lake. If the first 5 paddle strokes moves the kayak forward ten feet, and each additional 3 strokes moves the kayak an additional 8 feet. How far can the kayak move in 20 strokes?

6) On a ranch, there is an old hand pump. It takes Saraiah 6 pumps of the handle to get the first gallon of water. It takes 4 pumps of the handle for each additional gallon of water. If the handle is pumped 34 times, how many gallons of water will she have been pumped?

7) Nevaeh rented a bike. The fee was $8 for the first hour and $4.50 for each hour after the first hour. At the end of the ride, Nevaeh paid the bill of $26. How long had Nevaeh gone bike riding?

8) The cost of renting a power saw is $7 the first hour and $5.50 each additional hour. (a) If the saw is rented for 9 hours what is the total cost? (b) If the total cost of

renting the saw came to $29. How many hours was the saw billed for?

Linear Equations WS#11 (Word Problems) Name ______________________

Make a 3 column data table ( x , y1 , y2 ¿ with at least 3 values. The independent variable may start at 0. Find the SI equations for both y1∧ y2 . Solve by setting both equations equal to each other.

1) Mary can make wrap 1 candy bar per minute. Raquel can wrap 3 candy bars per minute. If Mary has a 10 candy bar head start, how many minutes will it take before Raquel can catch up to Mary?

2) A tree frog is 7 feet ahead of a bullfrog. Every time the tree frog jumps 2 foot, the bullfrog jumps 3 feet. How many times will the bullfrog have to jump to catch up with the tree frog?

3) Cricket "A" can jump 3 inches every jump; whereas cricket "B" can jump 8 inches every jump. If cricket "A" has a 20 inch head start, and each cricket jumps the same number of times, how many jumps will it take before cricket "B" can catch up to cricket "A"?

4) Ryan can move his canoe 3 feet forward for every paddle stroke he makes. His canoe partner, Matthew can move his canoe 5 feet forward for every paddle stroke he makes. If Ryan has a 40 foot head start, and each of them paddle the same number of times, how many paddle strokes will it take before Matthew can catch up to Ryan?

5) David has $120 in the bank and saves $10 every month. John has $60 in the bank and saves $20 per month. When will John have the same amount saved as David?

Linear Equations WS#12 Scatterplot Graphs – MPS and SI Name _______________________________________ Grade: _________

1) Identify the coordinates of the indicated points above. Use these coordinates to write the equation in MPS and SI. Do Check.

2) Use your SI equation to predict what salary an employee at this company would make, if he/she had worked at the company for 9 years?

3) Use your SI equation to predict how long an employee had worked at this company, if he/she made $55 thousand?

--------------------------------------------------------------

Age 10 11 5 15 14 3Height in Inches 57 60 43 68 66.5 40

4) Identify the coordinates of the indicated points above. Use these coordinates to write the equation in Modified Point Slope. Do a Check.

5) Use MPS to predict how tall a 9 year old would approximately?

6) Use MPS to predict approximately what age a person who is 33 inches tall to be?

Linear Equations WS#13 Scatterplot Graphs – MPS and SI Name _______________________________________ Grade: _________

1) Draw a line of best fit with a pencil. Identify two coordinates. Use these coordinates to write the equation in Modified Point Slope. Explain in a sentence what the slope number indicates specifically. Do a Check at 66 inches.

2) Use your MPS equation to predict how much a 5’8” tall (68 in.) woman would weigh. Compare to graph.

3) Use your SI equation to predict how tall a 135 lb. woman would be?

4) Using the plotted data points on the graph, how many women are actually 64 in tall?

5) Using the plotted data points on the graph, how many women weigh 155 lbs.?

6) Using the plotted data points on the graph, find the mode(s) of the heights.

7) Find the range of the weights.

8) Two women are 67 in. tall. How much does each woman weigh?

9) Use your MPS equation to predict the weight of a female you know. Determine if this prediction is accurate. How far off was the predicted weight from the actual? What other factors may can you think of that may affect the outcome?

10) What is the purpose of a scatterplot?

Linear Equations WS#14 Scatterplot Graphs – MPS and SI Name _______________________________________ Grade: _____

1) Is there a positive or negative correlation between a person’s age and the number of movies they go to?

2) Who will probably attend more movies in a year, a 15-year old or a 23-year old?

3) Identify two coordinates and find the slope. Explain in a sentence what the slope indicates specifically. Write the equation in both Modified Point Slope and Slope-Intercept. Do a check for a 22 years old and compare to graph.

4) Use your SI equation to predict the number of movies a 19-year old will attend in a year.

5) Use your SI equation to predict the age of a person who attends 18 movies per year.

-------------------------------------------------------------6) Use a pencil to label the scatterplot graph below. Draw

a line of best fit. Determine the type of correlation between the two sets of data.

7) What happens to the number of shots made as the distance from the basket increases?

8) Find the slope (4,18) and (16, 10). Next explain in a sentence what the slope means specifically.

9) Use these coordinates to write the equation in Modified Point Slope. Explain in a sentence what the slope number indicates specifically. Do a check at 22 feet from the basket.

10) How many predicted jump shots could be made from a distance of 25 feet from the basket? Show your work using your formula.

Distance from basket (ft.)

25 15 1 20 15 5 10 5 25

Jump shots made

6 10 15 7 12 18

13 20

5

Linear Equations WS#15 Scatterplot Graphs – MPS and SI Name _______________________________________ Grade: _____

1) Describe the Correlations.

2) Amco Bottling Co. is promoting a continuing education program for its employees. The personnel director, Ms. Smith would like to be able to predict an employee’s salary if she knows the number of year an employee attended college. From the current personnel files, Ms. Smith randomly selected the files of ten employees. She recorded each employee’s salary and corresponding years of college for the employee.

Make a scatter plot graph and determine a prediction equation in slope intercept form for this relationship.

a) Use your equation to predict the salary of an employee with 5 years of college education.

b) Predict how many years of college education a person has if they make a $27,000

3) The table below shows the heights and the corresponding ideal weights of adult women. Make a scatter plot graph and determine a prediction equation in slope intercept form for this relationship.

a) If someone was 5feet 10 inches tall (70 inches) how much would they be predicted to weigh?b) Predict how tall a person would be if they

weighed 90 pounds.4) The table below shows how typing speed and

experience are related. Make a scatter plot graph and determine a prediction equation in slope intercept form for this relationship.

a)I

f someone had 5 weeks experience predict how many words per minute they could type.

b) Predict how many weeks experience someone has who can type 50 words per minute.

5) The table below shows how sales of SUVs in the U.S. are related to the year.Make a scatter plot graph and determine a prediction equation in slope intercept form for this relationship.

a)E

xplain what the slope means as it relates to this problem (Do Not just state how to get slope).

b) Use your equation to predict the sales of SUVs in 2001.

c) What year does your prediction equation say it would be if there were 8 million in sales.

6) Make a scatter plot graph and determine a prediction equation in slope intercept form for this relationship.

StudentTime Spent

Watching TV (min.)

Time Spenton Homework

(min.)Sam 30 180John 45 150Laura 120 90Darren 240 30Megan 90 120Pia 150 120Crystal 180 90

Use your graph equation to predict:

Years of college

3 2 4 6 2.5 7.5 7 1 5.5 4

Salary (in $1000)

15 20 22 47 19 18 32 10 30 28

Height (inches)

60 62 64 66 68 70 72

Weight (pounds)

105 111 123 130 139 149 158

Experience(weeks)

4 7 8 1 6 3 5 2 9 6 7 10

Typing Speed (wpm)

33 45 46 20 40 30 38 22 52 44 42 55

Years 1991 1992 1993 1994 1995 1996 1997 1998 1999

Sales (in millions)

0.9 1.1 1.4 1.6 1.7 2.1 2.4 2.7 3.2

a) How much time would a student spend on homework if they watch 210 minutes of TV?

b) How much time would a student spend watching TV if they spend 120 minutes doing homework?

Documents

Name Unit 1 Post-Testpaulcamaren.wikispaces.com/file/view/SPP.Linear Equati… · Web view2018-03-14 · How many weeks will you have to save up your allowance in order to buy the