ALGEBRA I NOTES. Quarter 1. Name Teacher

Transcription

1 ALGEBRA I NOTES Quarter 1 Name Teacher 1

2 Table of Contents Unit 1 Solving Equations Two Step Equations page 7 Properties of Real Numbers page 8 Proof for Equations page 12 Solving Multi-Step Equations page 15 Word Problems with Proportions page 18 and Equations Unit 2 Solving Inequalities Linear Inequalities page 26 Compound Inequalities page 29 Word Problems with Inequalities page 33 Unit 3 Literal Equations Solving Literal Equations page 37 Introduction to Functions page 41 Functional Notation page 45 Unit 4 Graphing Linear Equations and Inequalities Graphing with Table of Values page 49 Graphing using Intercepts page 54 What is Slope? page 59 Graphing in Slope Intercept Form page 62 Graphing Linear Inequalities page 67 2

3 QR Code Reader Throughout the year, we will be using QR codes for video tutorials, in class activities and for posting review sheet answer keys. If you have not already, please download a free QR Code reader app to your mobile device. While this is not mandatory, it is very helpful. Here are some examples: QR Code Reader by Scan, Inc QR Code Reader TWMobile QR & Barcode Scanner Gamma Play.com 3

4 Warm-Ups 4

5 Warm-Ups 5

6 Extra Graph Paper 6

7 Two-Step Equations Learning Target: SOL A.4d: The student will solve multistep linear equations algebraically. Solve each equation. Leave all non-integer answers as fully simplified fractions Try It! Solve each equation. Leave all non-integer answers as fully simplified fractions

8 Properties of Real Numbers Learning Target: SOL A.4b: The student will justify steps used in simplifying expressions and solving equations. Review of properties! Identify the property displayed in each example. Example Property 8

9 Using the Distributive Property Multiplication with the Distributive Property: The first number is distributed across the parentheses by multiplying it with both of the numbers inside the parentheses. Simplify each expression. Combine like terms if necessary Division with the Distributive Property: The distributive property can also be used to simplify fractions with a monomial expression in the denominator. Instead of multiplying each coefficient, divide each coefficient by the number in the denominator Try it! Simplify the following expressions using the distributive property. Combine like terms when necessary

10 Properties of Equality A quantity is equal to itself. Quantities on each side of an equal sign may be switched. If a first quantity equals a second, and the second equals a third, then the first and third quantities are also equal. Equal quantities may be substituted for each other. x = x If x = y, then y = x. If a = b and b = c, then a = c. If y = 3, then 2y = 2(3). Try it! Identify the property displayed in each example

11 Properties Warm-Up! Identify the property displayed in each example Which property of real numbers justifies the work shown? 13x 1 = (12x + 15) + 7x 13x 1 = 7x + (12x + 15) A. Commutative property of addition B. Associative property of addition C. Identity property of addition D. Distributive property Simplify the following expressions using the distributive property. Combine like terms when necessary

12 Proofs for Equations Learning Target: SOL A.4b: The student will justify steps used in simplifying expressions and solving equations. Adding the same number to each side of an equation produces an equivalent equation. Subtracting the same number from each side of an equation produces an equivalent equation. Multiplying both sides of an equation by the same number produces an equivalent equation. Dividing both sides of an equation by the same number produces an equivalent equation. If a = b Then a + x = b + x If a = b Then a x = b x If a = b Then a x = b x If a = b Then What property is being used when simplifying the expression or equation below? David solved an equation as shown. What property justifies the work between Step 1 and Step 2? Step 1: x 12 = -9 Step 2: x = Step 3: x + 0 = 3 Step 4: x = 3 12

13 Proofs! Solve each two-step equation below. Justify each step in the boxes provided. Solution Justification Given Find all of the mistakes in the following proof. Identify and correct these mistakes. Given Symmetric Property of Equality Inverse Property of Addition Addition Property of Equality Additive Identity Property Division Property of Equality Inverse Property of Multiplication Multiplicative Identity Property 13

14 1. Justify the steps for proof in the boxes provided. Try It! Solution Justification Given 2. Find all of the mistakes in the following proof. Identify and correct these mistakes. Given Subtraction Property of Equality Additive Inverse Zero Product Property Division Property of Equality Multiplicative Identity Multiplicative Inverse 3. What property is being used when simplifying the expression or equation below? a. b. c. d. 14

15 Solving Multi-Step Equations Learning Target: SOL A.4d: The student will solve multistep linear equations in two variables including solving multistep linear equations algebraically and graphically. Solve each equation. Leave any non-integer answers as fractions unless decimals were used in the original problem. Round any decimals according to the decimals in the problem

16 Solve and discuss with your neighbor Using the given proof, justify each step in the boxes provided. Steps Justification Given 13. Using the given proof, justify each step in the spaces provided. Solution Justification Given 16

17 Try it! Solve each equation. Leave any non-integer answers as fully simplified fractions Jerri wrote these steps when solving an equation. Select a property from the box to justify each step. Write your answers in each box. Steps Justification Given Combine Like Terms Subtraction Property of Equality Additive Identity Division Property of Equality Distributive Property Associative Property 17

18 Using Equations and Proportions to Solve Word Problems Learning Target: SOL A.4f The student will solve realworld problems involving multi-step linear equations in two variables. Steps A. Define your variables. B. Use your variables to write an equation or proportion that represents the situation. Things to Remember! Perimeter of a rectangle: Angles in a Triangle: C. Solve your equation Consecutive Integers: D. Circle your final answer. Include units! 1. As a lifeguard, you earn $6 per day plus $2.50 per hour. How many hours must you work to earn $16 in one day? 2. The sum of the ages of three brothers is 59. Jason is twice as old as Brian. Alex is five more than three times Brian s age. How old is each brother? 18

19 3. The ship model kits sold at a hobby store have a scale of 1ft : 600ft. A completed model of the Queen Elizabeth II is 1.6 feet long. Estimate the actual length of the Queen Elizabeth II. 4. The perimeter of a rectangle is 168 feet. Its length is 5 times the width. Find the dimensions of the rectangle. 5. Mr. Kasman is trying to decide how many pizzas to buy for the 8 th grade picnic. If he usually needs 9 large pizzas to feed his class of 26 students, how many large pizzas should he buy if there are 204 students in the entire 8 th grade? 6. The sum of three consecutive integers is 270. Find the numbers. 19

20 7. Find three consecutive odd integers such that the sum of the third and three times the first is the same as thirty more than twice the second % of the books on Ms. Park s book shelf are mystery novels. If she has 40 books on her bookshelf, how many of them are mystery novels? 9. In triangle ABC the measure of angle B is fifteen degrees less than the measure of angle A. The degree of angle C is ten degrees more than the sum of the measures of angles A and B. How much does each angle measure? 10. Ed Sheeran s Instagram account gets forty new followers every 5 minutes. Which proportion shows the number of followers he will have after 1 hour? A. B. C. D. 20

21 Try It! 1. A lifeguard at the community pool makes $9.50 per hour. A lifeguard at the country club makes $8.25 per hour, but has a weekly bonus of $40. How many hours do the lifeguards need to work in one week to earn the same amount of money? 2. Triangle ABC and Triangle DEF are similar. The height of ABC is 4 cm and the base is 7 cm. If the height of DEF is 14 cm, how long is the base? 3. Find three consecutive even integers such that the sum of the first and twice the third is the same as twenty-eight less than four times the second. 4. Abby is five years older than Lindsay and Lindsay is 3 years older than Kaitlin. The sum of their ages is 32. Find their ages. 21

22 5. When Sarah went to college she had $15,000 in a savings account to pay the rent on her apartment. Every month she makes a $1,300 withdrawal to pay rent. If she only has $3,300 left, how many months has she been paying rent? 6. Brady is standing next to a flagpole that is 24 feet high. If the flagpole s shadow is 13 feet and Brady s shadow is 3 feet, how tall is Brady? Round to the nearest 100 th if necessary. 7. Danny bought a computer for $1,800. He made a down payment of $200 and will pay the rest in 5 equal payments. If p represents the amount of each payment, which equation can be used to find this amount? A. $200p = $1800 B. $ p = $200 C. $ $200 = 5p D. $1800 = 5p + $ Tara babysits every Saturday afternoon. She typically gets paid $42 for four hours worth of work. If she is asked to stay late, how much should she be paid for six hours worth of work? Which proportion correctly sets up this problem? A. B. C. D. 22

23 Equations Warm-Up! Solve each equation. Leave any non-integer answers as fully simplified fractions Makenna, Alexis, and Piper were solving three different math problems. The last step of their work is given below. Determine which person s problem has a solution that is all real numbers, whose problem has no solution and whose problem has the solution x = 0. Makenna Alexis Piper 6x = 0 0x = 5 5 = 5 5. Using the given proof, justify each step in the spaces provided. Solution Justification Given 23

24 6. Plumber Joe charges a flat fee of $45 plus $15 per hour for every house call he makes. If he charges Mr. and Mrs. Centennial $112.50, how many hours did he work at their house? 7. A person that weighs 135 pounds on earth would weigh pounds on the moon. What would a rock that weighs 7.06 pounds on earth weigh on the moon? 8. You purchase 4 tickets to a baseball game from an internet agency. In addition to the cost per ticket, the agency charges a convenience charge of $2.75 per ticket. You also choose to pay for rush delivery, which costs $18. The total cost of your order is $157. What is the price per ticket before the convenience charge? 9. John is eight years older than Henry and Henry is seven years older than Fred. The sum of their ages is 49. Find their ages. 24

25 Unit 1 Scratch Paper 25

26 Solving Linear Inequalities Learning Target: SOL A.5a: The student will solve multistep linear inequalities in two variables including solving multistep linear inequalities algebraically and graphically. Axioms of Inequality Adding or subtracting the same number to each side of an inequality produces an equivalent inequality. If a > b, then a + c > b + c. If a < b, then a c < b c. If you multiply or divide each side of an inequality by a.. Positive number you produce an equivalent inequality. Negative number you have to flip the sign to produce an equivalent inequality. If a < b and c is positive, then ac < bc. If a < b and c is negative, then ac > bc. Solving inequalities is very similar to solving equations with one notable difference! Graph the solution for number #4. Then give two possible values of x that will make the inequality true. 26

27 6. 7. Special Cases If the inequality is TRUE, the answer is: If the inequality is FALSE, the answer is: Using the axioms of inequality and the properties of real numbers, justify each step in the solutions given below. Solution Justification Given 27

28 Try it! Solve each inequality Graph the solution for number #1. Then give two possible values of x that will make the inequality true. 6. Using the axioms of inequality and the properties of real numbers, justify each step in the solutions given below. Solution Justification Given 28

29 Solving and Graphing Compound Inequalities Learning Target: SOL A.5a: The student will solve multistep linear inequalities in two variables including solving multistep linear inequalities algebraically and graphically. And Inequalities When two inequalities are joined by the word and, the solution of the inequality occurs when both inequalities are true at the same time. Translate and graph: x is at least negative six and at most five Solve each compound inequality Write an inequality that corresponds to the graph below. 29

30 Or Inequalities When two inequalities are joined by the word or, the solution of the inequality occurs when either of the inequalities is true. Translate and graph: x is either less than negative 2 or x is greater than seven Solve each compound inequality Write an inequality that corresponds to the graph below. 30

31 Special Cases for OR inequalities Solve and graph each compound inequality Try it! Solve each compound inequality Try its are continued on the next page! 31

32 Graph the answer to #3. 6. Graph the answer to #4. 7. Write an inequality that corresponds to each graph below: a. b

33 Using Inequalities to Solve Word Problems Learning Target: SOL A.5c: The student will solve realworld problems involving multi-step linear inequalities in two variables. Recognizing Inequalities x is at most 4 x is at least 4 x is no more than 4 x is no less than 4 1. Sally wants to rent tables for her outdoor wedding. The rental shop in town will charge her $11.25 to rent the long rectangular table for her bridal party that day. Each of the round tables her guests will sit at cost $8.75. If she can spend no more than $160 on tables, what are the possible numbers of round tables she can rent? Represent your answer algebraically and graphically. 2. A certain playlist can hold at most 70 minutes of music. So far you have downloaded 25 minutes of music onto the playlist. You estimate that each song lasts 4 minutes. What are the possible numbers of additional songs that you can download onto the playlist? 3. Charles is saving $20 each week. He earns an extra $80 by helping his neighbor landscape their yard. How many weeks will he need to save in order to have at least $400? 33

34 4. A gas station charges $0.10 less per gallon of gasoline if a customer also gets a car wash. The price of gas is regularly $2.09 a gallon, and a car wash is $8.00. If you get a car wash, what are the possible amounts (in gallons) of gasoline that you can buy if you can spend at most $20? 5. Your cell phone plan costs $49.99 per month for a given number of minutes. Each additional minute or part of a minute costs $0.40. You budgeted $55 per month for phone costs. What are the possible additional minutes (x) that you can afford each month? 6. To become a member of an ice skating rink, you have to pay a $30 membership fee. The cost of admission to the rink is $5 for members and $7 for nonmembers. After how many visits to the rink is it less expensive to be a member than a nonmember? In other words, at what point is it worth it to get the membership? 34

35 Try it! Write an inequality to represent each word problem below. Then, find the solution. SHOW ALL OF YOUR WORK! 1. Tony is a new waiter at the family restaurant in town. He is hoping to earn at least $100 during his 8 hour shift. If he makes $70 in tips, what would his hourly rate need to be to reach this goal? 2. Bryan s dog is three years more than twice his cat s age. Find all possible ages of the cat if the sum of their ages is at most Pretty Mountain State Park rents cabins for guests to stay in for $110 per night. If you have purchased a year-long state parks pass, they will discount your nightly rate by $15. At the time of rental, guests can also opt to pay $55 for an unlimited supply of firewood. You have a state parks pass and you will choose to pay for the unlimited supply of firewood. For how many nights can you rent the cabin if you are determined to spend less than $1,100? 4. The length of a rectangle is 6 inches more than the width. The perimeter of the rectangle can be no more than 48 inches. What is the maximum width? 35

36 Unit 2 Scratch Paper 36

37 Solving Literal Equations (Formulas) Learning Target: SOL A.4a: The student will solve literal equations (formulas) for a given variable. Rearrange a formula ( Solve the Formula ) so that a new variable is isolated. Backwards PEMDAS! Solve for the indicated variable. 1., solve for 2., solve for 3. solve for 4. solve for 5., solve for 6., solve for 37

38 Function Form: A two-variable equation (usually x and y) is written in function form if one of its variables is isolated on one side of the equation. Rewrite the following equations so y is a function of x. (Write y in terms of x in other words, isolate y!) Write all answers in simplest form! Millie was given the equation. Millie wants to isolate the variable y. What would be her first step? A. Divide by 3 on both sides. B. Add 7y to both sides. C. Subtract 3x from both sides. D. Add 3x to both sides. 38

39 Try it! Solve for the indicated variable The formula shown can be used to find, the amount of money Kyle has in his savings account. Kyle wants to find, the rate of interest his money earns. Which equation is correctly solves for? A. B. C. D. Try its are continued on the next page 39

40 Rewrite each equation so that y is a function of x. Write your answer in simplest form

41 An Introduction to Functions Learning Target: SOL A.7a and b: The student will investigate and analyze linear families and their characteristics both algebraically and graphically, including determining whether a relation is a function and finding the domain and range of a function. Relation any combination of inputs and outputs. Key Definitions Function A relation in which every is paired with only one! Ways to represent relations and functions: Every is a but not every is a! x y One Way Street! Only check the x s! Directions: Decide if the given values represent a function. Then, state the domain and range x y 3. x y

42 Vertical Line Test Function: Not a Function: Use the vertical line test to determine if the relation is a function

43 State the domain and range of each function D: D: R: 10. R: 11. D: D: R: 12. R: 13. D: D: R: R: 43

44 Try it! State the domain and range of each relation below. Then, determine if it represents a function. 1. {(-2, -8),(-1, -1), (0, 0), (1, 1), (2, 8)} 2. x y Draw the graph of a function with the following domain and range: 6. Using the ordered pairs shown, create a relation containing three ordered pairs with a range of {-1, 2, 4}. 44

45 Functional Notation Learning Target: SOL A.7e: The student will investigate and analyze linear families and their characteristics both algebraically and graphically, including finding the values of a function for elements in its domain. What is functional notation? The symbol is another name for y and is read as. It does not mean f times x. You can use letters other than f, such as g or h to name functions. Let f(x) = 4x 3 and g(x) = x Evaluate each function for the given x values. 1. f(-5) 2. g(4) 3. g(-3) 4. f(g(6)) Let f(x) = 6x + 9 and g(x) = -x + 5. Find the value of x so that the function has the given value. 5. f(x) = 3 6. g(x) = 2 45

46 Try it! Let f(x) = 2x and g(x) = 4x 6. Evaluate each function for the given domain values. 1. f(-4) 2. g(7) 3. g(f(3)) Let f(x) = -7x + 12 and g(x) = 8x 32. Find the value of x so that the function has the given value. 4. f(x) = g(x) = 4 6. True or False: A relation is always a function. Support your reasoning with an example or a counter-example. (Note: A counter-example is an example proving the statement is false.) 46

47 Functions Warm Up! Let f(x) = x 2 4x + 9 and g(x) = 2x + 3. Solve for the missing variable. 1. g(0) 2. g(f(-3)) 3. g(x) = 5 4. g(x) = 0 For questions 5 7: a. Determine if each relation graphed is a function b. State the domain and range of each relation x Function? D: R: Function? D: R: y Function? D: R: 47

48 Unit 3 Scratch Paper 48

49 Graphing Linear Equations Using a Table of Values Learning Target: SOL A.6, A.7e, f: The student will graph linear equations in two variables; find the values of a function for elements in its domain; and make connections between and among multiple representations of a function. The graph of an equation in two variables is the set of points in a coordinate plane that represents all solutions of the equation. Make a table of values for the following equations. Then, graph. 1. x y 2. x f(x) 49

50 Remember to always get y by itself! 3. x y 4. x y 50

51 Horizontal and Vertical Lines! Make a table of values for the following equations. Then, graph each equation. When given an equation x = #, let all values be the given number. When given an equation y = #, let all values be the given number x y x y x y x y 51

52 Try it! Make a table of values for the following equations. Then graph. 1. Use the domain {0, 1, 2, 3, 4}. x f(x) 2. Use the domain {-2, -1, 0, 1, 2}. x y 3. Graph using a table of values. x y 52

53 4. Choose your own domain. x y 5. Which of the graphs in #1 4 do not represent a function? Explain your reasoning. 6. Identify the graphs above that represent a function. State the domain and range of the graphs. 7. Write an equation for a function whose domain is all real numbers and whose range is 3. What kind of line is this? Graph the line. 53

54 Graphing Equations in Standard Form Using Intercepts Learning Target: SOL A.6, A.7f: The student will graph linear equations in two variables and make connections between and among multiple representations of a function. Standard Form: You can easily graph an equation written in standard form by finding two convenient points. X Intercept Y Intercept Draw the line that has the given intercepts. 1. x-intercept: 3 2. x-intercept:-4 y-intercept: 5 y-intercept: -2 Graph the following equations by finding the x- and y-intercepts

55 What are roots? Finding the Roots of a Function: Method 1: Graphically Find the root(s) of each graph. (In other words, find the x-intercepts.)

56 Method 2: Algebraically Find the root(s) of each equation.(in other words, find the solution when f(x)=0 or y=0.) Try It! 1. Graph the following equations. Label the points, using ordered pairs, where the line crosses the axes. A. B. C. D. 56

57 2. You are helping to plan an awards banquet for your school, and you need to rent tables to seat 180 people. Tables come in two sizes. Small tables seat 4 people, and large tables seat 6 people. This situation can be modeled by the equation Where x is the number of small tables and y is the number of large tables. Find the intercepts of the graph of the equation. Graph the equation. (Don t forget to label your x- and y- axis) Give four possibilities for the number of each size table you could rent. 3. Find the roots of the following functions: A. B. C. D. 57

58 4. Is it possible for a line not to have an x-intercept? Is it possible for a line not to have a y-intercept? Explain. 5. The x-intercept of the graph of Ax + 5y = 20 is 2. What is the value of A? 6. Consider the equation 3x + 5y = k. What values could k have so that the x- intercept and the y-intercept of the equation s graph would both be integers? Explain. 7. If a 0, find the intercepts of the graph of y = ax + b in terms of a and b. 58

59 What is slope? Learning Target: SOL A.6a The student will graph linear equations in two variables and determine the slope of a line when given the graph of the line or two points on the line. The slope of a non-vertical line is the ratio of the change to the change. We refer to this as the rate of change and use m to represent slope. Finding the Slope of a Line Given A Graph Read a graph like you read a book, from left to right. If the line is going, the slope should be. If the line is going, the slope should be. Positive Slope Negative Slope m = Find the slope of each line graphed

60 H O Y Finding Slope of Horizontal and Vertical Lines HOY V U X VUX Finding the Slope of a Line Given Two Points m = Find the slope of each line passing through the given points. 7. (4, 3) and (-2, -3) 8. (3, 5) and (8, 2) 9. (8, 0) and (8, 4) 10. (6, -2) and (5, -2) 60

61 Try it! Find the slope of each line What type of line has a slope of zero? 4. Is a line with an undefined slope a function? Why or why not? 5. Which line in the picture on the right has a slope of A. Line A B. Line B C. Line C D. Line D Find the slope of the line passing through the given points. 6. (-1, 2) and (3, -4) 7. (0, 5) and (-3, 5) 8. (8, 5) and (2, -7) 9. (-1, 3) and (-1, 9) 61

62 Graph Using Slope-Intercept Form Learning Target: SOL A.6a The student will graph linear equations in two variables including determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Graph the line y = 2x + 1. What is the slope of the line? x y What is the y-intercept? Slope-Intercept Form Directions: Identify the slope and the y-intercept for each equation. (Be sure to re-write it in slope-intercept form first!)

63 Directions: Graph each line using the slope-intercept method. Steps 1. Re-write equation in slope-intercept form. 2. Graph the y-intercept (this goes directly on the y-axis!) 3. Use the slope to find the next point. 4. Draw the line When visiting Baltimore, MD, you need to rent a taxi to get from your hotel to the National Aquarium. The taxi company charges a flat fee of $6.00 for using the taxi and $2.00 per mile. A. Write an equation in slope intercept form that models this situation. B. Graph the line. Don t forget to label each axis! (Count by 2 s on the y-axis!) C. After how many miles is the cost of your taxi ride $26? 63

64 Directions: Decide which method is most efficient. Graph using that method Method: Method: Method: Try it! Determine the slope (m) and y-intercept (b) of each line Graph each line using slope intercept form Try its are continued on the next page 64

65 Anna babysits every Saturday night. She charges a flat rate of $10, plus $8 per hour. A. Write an equation in slope intercept form that models the situation. B. Graph the line. Don t forget to label each axis! (Count by 2 s on the y-axis!) C. How much would Anna make if she babysits for 2 hours? 9. Jan pays $0.50 per hour to park her car at the museum. Which graph shows the relationship between the hours(x) Jan s car is parked and the total cost in dollars(y)? Graphing and Functions Warm Up 65

66 Graphing and Functions Warm-Up! Find the roots Find the domain and range of the graph in #3. D: R: 5. Let. If the domain is {-4, 0, 4}, find the range. 6. Find the x and y intercepts: 7. Graph using the most efficient method. 66

67 Graphing Linear Inequalities Learning SOL A.5a The student will solve multistep linear inequalities algebraically and graphically. Step 1: Decide if the line will be solid or dotted. < or > or When Graphing One Linear Inequalities Dotted line means all ordered pairs on the line! Solid line means all ordered pairs on the line! Step 2: Decide on the method of graphing. Step 3: Graph the line. Step 4: Shade appropriately. < or > or Use a ruler for precision! If y is, use the inequality symbol to determine the direction you should shade. If y is, flip the symbol! Then, determine the direction you should shade. Graph each linear inequality. Then, list 3 solutions to each inequality. A solution is an ordered pair! Is the line dotted or solid? Is the shaded region above or below the line? Is the line dotted or solid? Is the shaded region above or below the line? Possible Solutions: Possible Solutions: Linear inequalities have MANY solutions! Choose the obvious (in other words, points that are definitely in the shaded region). 67

68 3. 4. Possible Solutions: Possible Solutions: 5. Jackson can spend no more than $24 to buy pecans and cashews. He will pay $6 per pound for pecans and $8 per pound for cashews. a. Write an inequality that models this situation. b. Graph the linear inequality. Label your x and y-axis! c. Give two possible solutions for the amount of pecans and cashes Jackson is able to purchase. 68

69 Try it! Graph each linear inequality. Then, list 3 solutions to each inequality Is the line dotted or solid? Is the shaded region above or below the line? Is the line dotted or solid? Is the shaded region above or below the line? Possible Solutions: Possible Solutions: Hint: Decide whether you need to shade on the left or the right of the line. Possible Solutions: Possible Solutions: 5. Is the point (0, 3) a solution to the linear inequality graphed in #1? Why or why not? 6. Is the point (-2, 0) a solution to the linear inequality graphed in #2? Why or why not? 69

70 7. Which of the graphs below have (1,2) in their solution set? Circle all that apply. 8. Frank works at a convenience store. He earns $7.50 per hour when he works during the day. He earns $12.50 per hour when he works at night. He wants to earn at least $300 per week. Which graph best represents this situation? (Hint: set up an inequality first!) 70

71 Unit 4 Scratch Paper 71