Forms of Lines and Modeling Using Linear Equationsmath-mschernov.weebly.com/uploads/3/7/1/7/3717458/_unit_4_packet.pdf · Forms of Lines and Modeling Using Linear Equations Description:

UNIT4–Math621

Forms of Lines and Modeling Using Linear Equations

Description:

This unit focuses on different forms of linear equations. Slope- intercept, point-slope and standard forms are introduced. Students will write all three forms using short descriptions, tables of values and/or graphs. In addition, students will be able to transform one form into another and construct linear graphs for each form. They will be able to graph lines using the x and y- intercepts, a slope and y-intercept, a point and a slope or two points, accordingly to the given form of the equation. The unit will be concluded with an introduction to linear modeling, where students will recognize linear relationship between independent and dependent variables. Students will derive equations, graph functions and use their equations and graphs to make predictions. In the process of modeling, students will determine the constant rate of change and initial value of a function from a description of a relationship. They will interpret slope as rate of change, relate slope to the steepness of a line, and learn that the sign of the slope indicates that a linear function is increasing if the slope is positive and decreasing if the slope is negative.

4.1Slopeandslope-interceptformoflines4.2IvySmithPerformanceTask4.3Point-Slopeformoflines4.4StandardFormforlinesQuizonsections4.1-4.4

4.5Modelingusinglinearequations4.6MoreonModeling4.7UnitReviewUnit4TEST

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RESOURCES 4.1Slope-interceptformoflineshttps://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8th-slope-intercept-form/v/linear-equations-in-slope-intercept-form4.2Point-Slopeformoflineshttps://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/point-slope/v/idea-behind-point-slope-form4.3StandardFormforlineshttps://www.youtube.com/watch?v=3HdrW8f7Th8https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/standard-form/v/point-slope-and-standard-form4.4Reviewoflinearformshttps://www.youtube.com/watch?v=fLRkUmE07Jo4.5Modelingusinglinearequationshttps://www.youtube.com/watch?v=BR7MJpvUL0Q4.6MoreonModelinghttps://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8th-linear-functions-modeling/v/exploring-linear-relationships

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4.1SlopeFormulaandSlope-InterceptFormReview

The slope formula is: m = y2 − y1x2 − x1

for the points (x1, y1) and (x2, y2 )

Example: Find the slope of the line that goes through the points (5, -3) and (2, 3)

1:Usetheslopeformulatofindtheslopeofthelinethroughthegivenpoints.Leave answersinsimplifiedfractionalform.

1. A(3, 1) and B(5, -1)

2. C(7, 0) and D(5, -3)

3. E(7, 8) and F(3, 8)

4. G(-3, 5) and H(-3, 2)

5.(2,6)and(7,1)

6.(4,-1)and(0,9)

7.(3,7)and(4,7)

8.(7,2)and(7,-4)

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9.(3,-3)and(2,-2)

10.(7,0)and(2,10)

Rewrite each of these equations in slope-intercept form. 11. 3x – 4y = 24

12. x + 4y = 12

Use the slope formula to find the slope of the line going through each of these pairs of points. 13. A(7, 4) and B(-2, 1)

14. C(0, 3) and D(4, 0)

Identify the type of line (vertical,horizontaloroblique)forthegivenequations. 15. y = 3x + 4 vertical horizontal oblique

16. 3x = 7y vertical horizontal oblique

17. 3y = 9 vertical horizontal oblique

18. x = 3 vertical horizontal oblique

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Identify the slope and y-intercept of the lines represented by each of these equations. 19. y = 4x + 7 slope = ________ y-intercept = ________

20. 3x + 2y = 12 slope = ________ y-intercept = ________

21. x = 10 slope = ________ y-intercept = ________

22. y = 3 slope = ________ y-intercept = ________

Findtheequationofeachlineinslope-interceptform 23.Thelinehasaslopeof7anday-interceptat-2. ________________________________________ 24.Theslopeis-2anditgoesthroughthepoint(0,3).________________________________________ 25.Theslopeis5anditgoesthroughthepoint(2,-1) ________________________________________ Writetheequationofeachlineinslope-interceptform.

26.

27.

6

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Section 4.3 – Point-Slope Form Notes and Practice Lines of the form _____________________ are written in ______________________ form. Example 1: Write an equation for the line with slope = 2, that goes through the point (7, 3)

Example 2: Write an equation for the line with slope = 23

, that goes through the point (5, -6)

Example 3: Write an equation for the line with slope = -4, that goes through the point (-2, 1) In order to write the equation of any line you need _______________ and the ____________. If you are given both of those things, as you were above, then it’s easy to use the point-slope form of the line. Sometimes you aren’t actually given the information out-right, but you can figure it out from other information.

Example 4: Write an equation for a line that goes through the points (1, 3) and (-2, 2).

You have a point – in fact, you have two points from which to choose, but you need __________________________________. Fortunately, you can compute it: Let’s use the first point: __________________ with the slope ________________. The equation is: ___________________________________________________

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Example 5: Write an equation for a line that goes through the points (4, -5) and (2, 3): Example 6: Write an equation for a line that goes through the points (1, 3) and (7,3): Example 7: Write an equation for a line that goes through the points (1, 3) and (1,4):

It is easy to graph lines that are written in point-slope form. Just plot the point and use the slope. Example 8:

a. Graph the line y − 2 = 12(x + 5)

The slope is: _______ a point is _________

b. Graph the line y − 3= −2(x −1) The slope is: _________ a point is _________

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PRACTICE Find an equation for the line with the given information. Write your answer in whatever form is easiest. Note: Parallel lines have the same slope! 1. slope -1, through (5, -2)

2. slope: 54

, through (7,2)

3. through (1, 3) and (-2, -5) 4. through (1, 5) and (-2, 5) 5. slope: -2; y-intercept 5 6. slope = 4, through (0, 0) 7. through (3, 4) with undefined slope

8. parallel to y = 2x – 7 with y-intercept 5

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9. Graph the following lines. a. y +1= 2(x − 4)

b. y + 4 = 23(x − 2)

10. Write the equations of these graphs in point-slope form. a.

b.

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4.4-StandardFormforLines Notes

Therearethreecommonformsfortheequationsoflinesthatwewillbeusingthisyear.Forthepurposesofdefinition,coordinatesofpointsareindicatedbytheletters____&____.Constantsareindicatedbytheletters_____,_____and_____.Weusetheletter_____forslope.NotethatcapitalBstandsfor_____________________andlowercasebstandforthe______________.Itisimportantthatyoubeconsistentwithhowyouwritetheletters.

Name GeneralForm SpecificExample

Slope-intercept

TodaywewillfocusonSTANDARDform. IfyouareaskedtowritealinearequationinSTANDARDform,youmustdothreethings:

1.Eliminatefractionsbymultiplyingacrossbytheleastcommonmultipleofthedenominators.Youmayhavetodistributefirst,iftheequationisinpoint-slopeformtostart.

2.Movetermswithxandytotheleftandallconstantstotherightusing addition/subtraction.3.Makethefirsttermontheleftthetermwiththexandmakeitpositiveifitisnegativebymultiplyingeverythingbynegative1.

Example1.Writetheequationoftheline y = 23x − 4 inStandardform.

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Example2.Writetheequationoftheline y − 3= 12(x − 4) inStandardform.

Example3:Writetheequationoftheline 2y −23x = 4 inStandardform.

Given the graph find equation in Ax + By = C form. 4.

5.

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6.

Standardformisparticularlygoodforfindingx-interceptsandy-interceptsoflines. Rememberthataninterceptisthepointwherea__________________crossesan_________________. Anx-interceptisthepointwherea____________________crossesthe__________-axis. Ay-interceptisthepointwherea____________________crossesthe__________-axis. Example7.Findthex-interceptandthey-interceptoftheline4x+6y=12 •Tofindthex-intercept,substitute0inforthe_________value. Thex-interceptis_____________. •Tofindthey-intercept,substitute0inforthe_________value. They-interceptis_____________. Example8.Findthex-interceptandthey-interceptoftheline2x–3y=24 •Tofindthex-intercept,substitute0inforthe_________value. Thex-interceptis_____________. •Tofindthey-intercept,substitute0inforthe_________value. They-interceptis_____________.

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Example9.Findthex-interceptandthey-interceptoftheline-3x+6y=36 Thex-interceptis_____________. They-interceptis_____________.Example10.Graphthelinex - 5y = 10. Hint: find the x-intercept (make y= 0 in equation and solve for x) and

y-intercept (make x= 0 in equation and solve for y)

y-intercept!x-intercept!10. Graphtheline3x – 2y = 6 y-intercept!x-intercept!

X Y

0

0

X Y

0

0

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Section4.4Classwork Statethenamefortheformofthelineshownbelow. 1.y=mx+b _________________________________________________ 2.Ax+By=C _________________________________________________ 3. y – y1 = m x – x1( ) _________________________________________________ RewritetheseequationsinStandardForm

4.y=2x–5 ______________________________

5.y=15x+3 ______________________________

Findthex-interceptandthey-interceptoftheselines.

x-intercept y-intercept

6.6x–2y=12

7.3x+4y=9

8.y=6

9.x=2

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Usethexandyinterceptstographthesetwolines.10.4x–3y=6

11.5x+2y=15

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Section4.1-4.4QuizReview&StudyGuide 1.Youshouldknowthenames(includingspelling)andgeneralformsforeachofthethreeformsoflinearequationswehavestudiedinthisunit.Youshouldalsobeabletoprovideaspecificexample,usingnumericalvaluesasconstants.Youshouldknowthedifferencebetweenageneralformandspecificexampleofanequation.Fillinthemissinginformation:

Name GeneralForm SpecificExample

a. Slope-intercept

b.

(y − y1) = m(x − x1)

c. 2x+3y=12

2. Given the Standard Form of a line, you should be able to find the slope, x-intercept and y-

intercept of the line it represents.

Findtheslope,x-interceptandy-interceptforeachoftheselines.LinearEquation Slope x-intercept y-intercepta. 3x + 4y = 24

b. 5x − 3y = 30

c. x + 2y = 1

d.6x −10y = 30

e. 8x + 4y = 64

f. 7x − 7y = −21

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3. You should be able to convert from one form of a linear equation to another form. Convert these linear equations to Standard Form.

a.y = 7x - 6

b.y + 12 = -2(x+3)

c. y +34x = 1

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d.−2y + 13x = 5

4.Givenalineinstandardform,youshouldbeabletodrawitsgraphusingthex-intercept&y-intercept.

a.6x -10y = 30

b.7x + 3y = - 21

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5. Given the graph of a line, you should be able to identify its x-intercept, y-intercept and slope. You should also be able to write its equation in all 3 linear forms.

a) x-intercept = ___________ b) y-intercept = ___________ c) slope = ________________ d) Write the equation of the line

in point-slope form. e) Write the equation for the line in slope-intercept form. f) Write the equation for the line in standard form. 6. Given information about a line, you should be able to write its equation in point-slope, slope-

intercept and Standard forms. a. Write an equation for the line that passes through (1, -3) and has slope = –6 in point-slope

form. b. Write an equation for the line that passes through (3, 2) and has slope = − 1

3 in point-slope

form. c. Write an equation for the line passing through the points (2, 5) and (-3, 1) in point-slope form. d. Write an equation for the line that passes through (-1, 3) and has slope = 2 in slope-intercept

form.

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7. You should be able to graph lines presented in all three forms of linear equations.

Graph the following lines. a. 4x + 3y = 12

b. y = 34x − 2

c. (y − 3) = − 12(x + 4)

d. (y +1) = 2(x + 5)

e. y = 4

f. −2x + 3y = 6

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ANSWERS

1a. Slope-intercept y = mx + b y = 4x + 3 1b. Point-slope (y − y1) = m(x − x1) (y −1) = 2(x − 3) 1c. Standard Ax + By = C 2x + 3y = 4

LinearEquation Slope x-intercept y-intercept2a. 3x + 4y = 24 -3/4 8 62b.5x − 3y = 30 5/3 6 -102c. x + 2y = 1 -1/2 1 ½2d. 6x −10y = 30 3/5 5 -32e.8x + 4y = 64 -2 8 162f. 7x − 7y = −21 1 -3 3

3a. 7x – y = 6 3b. 2x + y = -18 3c. 9x +12y = 4 3d. x – 6y = 15

4a. 4b. 5. 6.

a. 2.5 b. 5 c. -2 d. y − 3= −2(x −1) e. y = −2x + 5 f. 2x + y = 5

a. y + 3= −6(x −1)

b. y − 2 = − 13(x − 3)

c.

y −1= 45

(x + 3)

or

y − 5 = 45

(x − 2)

d. y = 2x + 5 7a. 7b. 7c. 7d.

7e. 7f.

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4.6 Linear Functions as a Model We will continue to use these formulas in this section:

• Slope Formula:

• Slope-intercept form for a line: y = mx + b , where m is slope and b is the y − intercept • Standard form for a line: Ax + By = C , where A is positive • Point-Slope form for a line: y − y1 = m(x − x1) , where (x1, y1) is a point on the line Definitions: Independent Variable: Dependent Variable: Example A

Identify the independent (x) and dependent (y) variables in each situation.

1) Ben collects 3 stamps every month. The number of stamps collected depends on the number of years he keeps his hobby.

x=_____________________________________________________

y=_____________________________________________________

2) Masha plans to decorate her living room area with a carpet, but she is undecided on the length of carpet she will buy. The carpet she likes costs $10 per square foot.

x=_____________________________________________________

y=_____________________________________________________

3) Stephanisplacingmaskingtapearoundcircularmirrors.Hewantstofindthe amountoftapetopurchasebymeasuringtheradiiforeachmirror. x=_____________________________________________________

y=_____________________________________________________

m = y2 − y1x2 − x1

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4) A woman plans to travel to the Dominican Republic in 6 months for a family reunion. She wants to estimate the travel cost by surveying her family members who have already bought airline tickets about the total cost. She also asked them how many people are traveling in their groups.

x=_____________________________________________________y=_____________________________________________________

5. Axel’s Warehouse has banquet facilities to accommodate a maximum of 250 people. When the manager quotes a price for a banquet she is including the cost of renting the room plus the cost of the meal. A banquet for 70 people costs $1300. For 120 people, the price is $2200.

Let p to be the number of people and c the total cost. (a) Determine the dependent variable and independent variable. Independent = ____________________________________ Dependent =______________________________________ (b) Identify two points discussed in the problem above. ____________ and _____________ (c) Determine the slope of the line. (d) What does the slope of the line represent? (e) Construct an equation and rewrite it in slope-intercept form. (f) Plot a graph of cost versus the number of people. (g) What is the y-intercept? ____________ What does it mean? ___________________________________________________________ (h) Use your equation from part (e) to find the cost of a banquet for the maximum capacity of people for this facility.

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6. When a 40 gram mass was suspended from a coil spring, the length of the spring was 24 inches. When an 80 gram mass was suspended from the same coil spring, the length of the spring was 36 inches.

(a) Identify the independent variable and dependent variable in this problem x = ______________________________ y =_______________________________ (b) Graph the line, label the x and y axes. (c) Estimate the length of the spring for a mass of 70 grams and 90 grams based on the graph.

for 70 grams: _________________ for 90 grams: _________________ (d) Determine an equation that models this situation. Write the equation in slope-intercept form.

(e) Use the equation to find the length of the spring for a mass of 70 grams and 90 grams. Are these exact answers the same as your estimated ones from part (b)?

for 70 grams: _______________________________________________________ for 90 grams: _______________________________________________________ (f) What is the x-intercept? ___________ What does it represent? ____________________________________________________

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7.Jasonleaveshissummercottageanddriveshome.Afterdrivingfor5hours,heis112kmfromhome,andafter7hours,heis15kmfromhome.Assumethatthedistancefromhomeandthenumberofhoursdrivingformalinearrelationship.

a.Statethedependentandtheindependentvariables. dependentvariable: _____________________________________________________ independentvariable: _____________________________________________________ b.Whatarethetwopointsgiven? point1:___________________ point2:__________________ c.Whatistheslopeandwhatdoesitmeaninthisproblem? d.Determineanequationtomodelthissituation. e.Findthedistance-intercept(whendistance=0)andexplainwhatitrepresents. f.HowlongdidittakeJasontodrivefromhissummercottagetohome?

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4.7 More Modeling We will continue to use these formulas in this section: (Fill the blanks)

• Slope Formula: _________________________________________________ • Slope-intercept form for a line: ______________________________________ • Standard form for a line: ___________________________________________ • Point-Slope form for a line: _________________________________________

1. A rental car company offers a rental package for a midsize car. The cost is comprised of a

fixed $30 administrative fee for the cleaning and maintenance of the car plus a rental cost of $35 per day.

a. What is the dependent variable? __________________________________________ b. What is the independent variable? ________________________________________ c. What is the slope? d. What does the slope mean in the context of this problem? e. Determine an equation to model the relationship between the number of days and the total cost of renting a midsize car.

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2. The same company is advertising a deal on compact car rentals. The linear function 𝑦= 30𝑥 + 15 can be used to model the relationship between the number of days (𝑥) and the total cost (𝑦) of renting a compact car. a. What is the fixed administrative fee? ____________________ b. What is the rental cost per day? ___________________ c. What is the y-intercept? ____________ d. What is the slope and what does it mean in this problem? slope = ____________ It means . . .

___________________________________________________________________________

3. In 2008, a collector of sports memorabilia purchased 5 specific baseball cards as an investment. Let 𝑦 represent each card’s resale value (in dollars) and 𝑥 represent the number of years since purchase.

Each of the cards’ resale values after 0, 1, 2, 3, and 4 years could be modeled by linear

equations as follows:

Card A: 𝑦 = 5 − 0.7𝑥 Card B: 𝑦 = 4 + 2.6𝑥 Card C: 𝑦 = 10 + 0.9𝑥 Card D: 𝑦 = 10 − 1.1𝑥 Card E: 𝑦 = 8 + 0.25𝑥 a. Which card(s) are decreasing in value each year? ____________ How can you tell? b. Which card(s) had the greatest initial values at purchase (at 0 years)? ________

c. Which card(s) is increasing in value the fastest from year to year? ___________ How can you tell?

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d. If you were to graph the equations of the resale values of Card B and Card C, which card’s graph line would be steeper? Explain. e. Write a sentence that explains the 0.9 value in Card C’s equation ______________________________________________________________________________ 4. A car starts a journey with 18 gallons of fuel. Assuming a constant rate, the car will consume

0.04 gallons for every mile driven. Let 𝐴 represent the amount of gas in the tank (in gallons) and 𝑚 represent the number of miles driven.

a. State the dependent and the independent variables. independent: ____________________________________________ dependent: ______________________________________________ b. How much gas is in the tank if 0 miles have been driven? _________________ How would this be represented on the axes above? c. What is the rate of change that relates the amount of gas in the tank to the number of miles

driven? Explain what it means within the context of the problem.

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d. On the axes below, draw the line, or the graph, of the linear function that

relates 𝐴 to 𝑚.

e. Write the linear function that models the relationship between the number of miles driven and the amount of gas in the tank.

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5. Andrew works in a restaurant. The graph below shows the relationship between the amount Andrew earns and the number of hours he works.

a. If Andrew works for 7 hours, approximately how much does he earn? ________________

b. Estimate how long Andrew has to work in order to earn $64. ________________

c. What is the rate of change of the function given by the graph? _____________

d. Interpret the value of the rate of change within the context of the problem.

e. Record the coordinates of any two points from the graph. Point 1: _______________ Point 2: _______________

f. Compute the slope using the two points. (check your answer with your answer in (c)).

g. Write linear function that models the relationship in the story using two points written in (e).

h. What is the name of the form of the linear function you used? _____________________

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4.8Unit4ReviewYoushouldknowthenamesandformsofeachofthethreetypesofequationswestudiedinthisunit.Statethenamefortheformofthelineshownbelow.1.y=mx+b ____________________________________________2.Ax+By=C ____________________________________________3. y – y1 = m x – x1( ) ____________________________________________Youshouldbeabletoidentifytheslope,x-interceptandy-interceptforanequationwritteninanyoftheformatswehavestudiedFindtheslope,x-interceptandthey-interceptoftheselines. slope x-intercept y-intercept

4.5x–2y=20

5.4x+6y=24

6.x=10

7.y=7

8.y+7=5(x+1)

9.3x+6y=12

10.3x=-15

11.y–x=0

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Youshouldbeabletocomputetheslopeofalinethatgoesthroughtwogivenpoints.Findtheslopesofthelinesthatgothroughthesepoints.12.(6,0)and(2,-12)

13.(-5,0)and(0,15)

14.(8,1)and(12,1)

15.(3,-5)and(3,6)

Youshouldbeabletorecognizethemostefficientformtousetowriteanequationforalinegiveninformationaboutitandthenwritetheequationcorrectly.Giveanequationforeachoftheselines,giventhefollowingcharacteristics:16.Horizontallinethroughthepoint(7,4) ______________________________________________17.Verticallinethroughthepoint(9,10) ______________________________________________18.Alinethroughthepoints(7,4)and(9,10) ______________________________________________19.Alineparalleltotheliney=4x+5and throughthepoint(1,8) ______________________________________________

20.Alinewithslope= 25,throughthepoint(8,3)____________________________________________

21.Alinewithslope=4,withy-intercept(0,5) ______________________________________________ 22.Alineparalleltotheline2y–5x=14and

throughthepoint(-5,-2) ______________________________________________

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Youshouldbeabletotransformlinearequationswritteninoneformtotheotherforms.23.Thislineiswritteninpoint-slopeform.

RewriteitinSlope-InterceptFormANDinStandardForm.

Point-Slopeform: y–4= 23

(x −1)

Slope-Interceptform:_________________________ Standardform:_____________________________

Youshouldbeabletographlinesgiventheirequationsinanyformat.

24.Graphbothoftheselinesonthesamegrid:y=3andx=-4Fory=3slope:_______y-intercept:________Forx=-4slope:_______y-intercept:________

25.Graphtheliney= − 2

3x–3

Fortheliney= − 2

3x–3

slope:_______y-intercept:________

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26.Graphtheliney+3=¼(x+7)

27.Graphtheline-8x+4y=12

Youshouldbeabletowritetheequationofalinegivenitsgraph.Writetheequationofeachlineinslope-interceptform(y=mx+b).28.

Slope:y-intercept:Equation:

29.

Slope:y-intercept:Equation:

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Writetheequationofeachlineinpoint-slopeform y − y0 = m(x − x0 )

30.

31.

Youshouldbeabletoapplyyourknowledgeoflinearfunctionstoapplications.

32.Manycellphonecompanieshaveyoupayamonthlyfeethatentitlesyoutoacertainnumberof'free'minutesofuseduringthatmonth.Youpaythefeewhetheryouusetheservicefor1minuteor1hour.Youevenpaythefeeifyouneverplaceaphonecallatallduringaparticularmonth.However,ifyouusemorethantheincludedtime,youarechargedforyourextrause.

Supposeyougetacellphoneplanandpayamonthlyfeeof$39.95.Youget400'free'

minutesforthismoney.However,ifyouusemoretime,youarechargedatarateof$0.35(35cents)aminute.a.Whatwillbeyourbillifyouusetheservicefor3hoursonemonth?b.Whatwillbeyourbillifyouusetheservicefor450minutesonemonth?

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c.DrawtherelationbetweentheCharge(C)andthenumberofhours(h).

Besuretoputalabelandunitsonyourverticalaxis.Remember:Thereare60minutesinanhour.

33.TheSuperVinesmallfarmhas3lbs.ofveggiesinthecompostbinanditisrecycling2lbs.perday.Afruitstandnearbyhasplaceinitscompostbin4lbs.ofdamagefruitsandrecycles3lbs.eachday.a.Makeanequationforthenumbernpoundsofrecyclematerialeachbusinesshasafterddays.b.Graphtheequationsfromparta.(Considerifthegraphisdiscreteorcontinuous)

c.After5days,howmuchrecycledmaterialhasbeenplacedineachcompostbin?

123456789101112hours

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ANSWERS1.slope-interceptform 2.StandardForm 3.point-slopeform

4.slope= 52,x-intercept=(4,0),y-intercept=(0,-10)

5.slope=− 23,x-intercept=(6,0),y-intercept=(0,4)

6.slope=undefined,x-intercept=(10,0),y-intercept=none7.slope=0,x-intercept=none,y-intercept=(0,7)

8.slope=5,x-intercept=( 25,0),y-intercept=(0,-2)

9.slope=− 12,x-intercept=(4,0),y-intercept=(0,2)

10.slope=undefined,x-intercept=(-5,0),y-intercept=none11.slope=1,x-intercept=(0,0),y-intercept=(0,0)

12.m = −12 − 02 − 6

= −12−4

= 3 13.m = 15 − 00 − (−5)

= 155

= 3

14.m = 1−112 − 8

= 04= 0 15.m = 6 − (−5)

3− 3= 110= undefined

16.y=4 17.x=9 18.y–4=3(x–7)ory–10=3(x–9) 19.y–8=4(x–1)

20. y − 3= 25(x − 8) 21.y=4x+5or-4x+y=5 22, y + 2 = 5

2(x + 5)

23.Slope-intercept: y = 23x + 10

3 Standard:2x–3y=-10

24.fory=3:slope:0 y-int=(0,3); 25.slope=− 23 y-int=(0,-3)

forx=-4:slope=undefined y-int=none

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26. 27.

28. y = 34x − 3 ; slope= 3

4 y-int=(0,=3)

29. y = − 14x + 2 slope=− 1

4 y-int=(0,2)

30. y = − 25x − 3 or y + 5 = 2

5(x − 5) 31. y = 3

5x +1 or y − 4 = 3

5(x − 5)

32a.Cost=39.35 32b.Cost=$39.95+0.35(50)=$57.4532c.

33.a.n1 = 3+ 2dn2 = 4 + 3d

33b.discrete

33c.n1 = 3+ 2(5) = 13n2 = 4 + 3(5) = 19