Modeling Relationships 1. What is a function? 2. What is a linear function? How can you determine if a function is linear or not? 3. How can you determine the rate of change given the equation of a linear function? Interpreting with Functions Classwork 1. What is the slope of the table? x y -2-4 -1-1 0 2 1 5 2 8 Modeling with Equations Chapter Problems 2. What is the y-intercept of the table? x y -2-4 -1-1 0 2 1 5 2 8 3. A cell phone company charges $89.99 for a new phone and then $19.99 per month. What is the slope or rate of change for this situation? 4. A cell phone company charges $89.99 for a new phone and then $19.99 per month. What is the y- intercept or starting point for this situation? NJ Center for Teaching and Learning ~ 1 ~ www.njctl.org
5. What is the slope of the graph? 6. What is the y-intercept of the graph? 7. Joe was given $20 for his birthday. He then saved money from his allowance which was $10 per week. Identify the y-intercept and the slope for this situation. Homework 8. What is the slope of the table? x y -2-6 -1-5 0-4 1-3 2-2 9. What is the y-intercept of the table? x y -2 18-1 12 0 6 1 0 2-6 10. A plumber charges $75 for an initial house call and then $150 per hour. What is the slope or rate of change for this situation? NJ Center for Teaching and Learning ~ 2 ~ www.njctl.org
11. A plumber charges $75 for an initial house call and then $150 per hour.. What is the y-intercept or starting point for this situation? 12. What is the slope of the graph? 13. What is the y-intercept of the graph? 14. Jillian purchased a car for $1500. After she drives it off of the lot, it begins to depreciate at a rate of $120 per year. Identify the y-intercept and the slope for this situation. Analyzing Graphs Classwork 15. This graph could show the number of students enrolled in a college course over the semester? True or false? NJ Center for Teaching and Learning ~ 3 ~ www.njctl.org
16. This graph could show a person s savings over 10 years. True or false? 17. This graph could show the time and speed of a car including two stops along the way. True or false? Determine which are the dependent variable and the independent variable 18. The distance a car travels over a period of time. 19. The cost of a picnic and the number of people attending. 20. Your pay and the number of hours worked. Determine if each equation has a positive or negative rate of change. 21. y = 3x + 4 22. y = ½ x 6 23. y = -7x + 2 24. y = 2/3x 1 T/F the ordered pairs listed show a positive slope. 25. (1,2) (2,3) (3,4) (4,5) 26. (-1,-6) (-2,-4) (-3, -2) (-4,0) 27. (0,-8) (-1,-7) (-2,-6) (-3,-5) NJ Center for Teaching and Learning ~ 4 ~ www.njctl.org
Homework 28. This graph could show the number of people attending a party and the cost of the party. True or False? 29. This graph could show the height of a ball dropped from a certain height over a period of time. True or False? 30. This graph could show water temperature over a number of days. True or False? Determine which are the dependent variable and the independent variable. 31. Cellular data used and the bill for your cell phone. 32. Distance traveled and the amount of gas in your tank. 33. Annual cost of car insurance and the number of accidents you have had. NJ Center for Teaching and Learning ~ 5 ~ www.njctl.org
Determine if each equation has a positive or negative rate of change. 34. y = -.5x - 4 35. y = 10x + 4 36. y = -2x 37. y = 7/8x + 4 T/F the ordered pairs listed show a positive slope. 38. (8,4) (10,5) (6,12) (14,7) 39. (-1,1) (-2,2) (-3, 3) (-4,4) 40. (5,-12) (4,-14) (3,-16) (2,-18) Comparing Rates of Change Classwork 41. Which has the greater rate of change, the graph or the equation? y = 2x + 1 42. Which has the greater rate of change, the table or the equation? x -9-6 -3 0 3 6 9 y -4-3 -2-1 0 1 2 y = -2x - 1 43. Which has the greater rate of change, the situation or the equation? Stephanie climbs two steps at a time. y = -2x + 5 NJ Center for Teaching and Learning ~ 6 ~ www.njctl.org
Homework 44. Which has the greater rate of change, the graph, the equation or the ordered pairs? y = 6x + 4 (0,3) (3,6) (6,9) (12,12) 45. Which has the greater rate of change the situation or the ordered pairs? The cost of going to the movies is $8 per person (0,0) (1,7) (2,14) (3,21) NJ Center for Teaching and Learning ~ 7 ~ www.njctl.org
Modeling Relationships Unit Review PMI 8 th Grade Math Name Multiple Choice Choose the correct answer for each question. No partial credit will be given. 1. Find the slope of the chart. x y -2 18-1 12 0 6 1 0 2-6 a. -6 b. 0 c. 6 d. 1 6 2. Find the slope of the graph. a. -1 b. - 1 2 c. 1 2 d. 2 Short Constructed Response Write the correct answer for each question. No partial credit will be given. 3. Determine what the dependent and independent variables are: The age of a child and their height. Dependent Independent 4. Determine what the dependent and independent variables are: At the deli counter, the price of the meat and its weight. Dependent Independent NJ Center for Teaching and Learning ~ 8 ~ www.njctl.org
5. Give an example of a linear equation with a positive slope. 6. If a linear equation is y = 5x - 7, what is the y-intercept? 7. If a linear equation is y = - 4 x - 5, what is the slope? 3 8. A cell phone company charges $199.99 for a new cell phone and then $29.99 per month. If you were to write the equation to represent a monthly phone bill, what is the y-intercept? 9. A cell phone company charges $199.99 for a new cell phone and then $29.99 per month. If you were to write the equation to represent a monthly phone bill, what is the slope? 10. Which has the greater rate of change, the graph, the equation, or the ordered pairs? (0,3), (3,6), (6,9), (12,12) y = -3x + 7 NJ Center for Teaching and Learning ~ 9 ~ www.njctl.org
Extended Constructed Response - Solve the problem, showing all work. Partial credit may be given. 11. Your parents are looking to rent a car for their upcoming vacation. They want your help in comparing the prices between two companies renting the same car. The first dealership called Cars R Us charges an initial fee of $150 and then $99 a day. The second dealership called Car Mart charges an initial fee of $125 and then $115 a day. a. Identify the independent variable for Cars R Us. b. Identify the dependent variable for Car Mart. c. What is the slope of the equation for Car Mart? d. What is the y-intercept of the equation for Cars R Us? e. Fill in the table of values below. Day Cars R Us Car Mart 1 2 3 4 5 f. Explain which company is the better choice to use during your vacation. NJ Center for Teaching and Learning ~ 10 ~ www.njctl.org
12. You want to have fun in the water for your upcoming birthday party. Your parents gave you the choice of either heading to the local water park or renting out the community pool. The water park charges a setup fee of $85 and $7.50 per person. The pool charges a setup fee of $50 and charges $11 per person. a. Identify the independent variable for the pool. b. Identify the dependent variable for the water park. c. What is the slope of the equation for the water park? d. What is the y-intercept of the equation for the pool? e. Fill in the table of values below. People Pool Water Park 5 10 15 20 25 f. Explain which company is the better choice to use for your birthday party. NJ Center for Teaching and Learning ~ 11 ~ www.njctl.org
Answers 1. 3 2. 2 3. $19.99 4. $89.99 5. 2 6. 5 7. Slope = 10 y-int = 20 8. Slope = 1 9. y-int = 6 10. Slope = 150 11. y-int = 75 12. Slope = 2 13. y-int = 3 14. y-int = 1500; slope = -120 15. True 16. True 17. False 18. Time is independent and distance is dependent 19. People is independent and cost is dependent 20. Hours is independent and pay is dependent 21. Positive 22. Positive 23. Negative 24. Positive 25. 1 True 26. -2 False 27. -1 False 28. True 29. True 30. True 31. Data is independent and bill is dependent 32. Distance is independent and gas is dependent 33. Accidents are independent and cost of insurance is dependent 34. Negative 35. Positive 36. Negative 37. Positive 38. ½ True 39. -1 False 40. 2 True 41. Equation 42. Equation 43. They are the same 44. Equation 45. Situation NJ Center for Teaching and Learning ~ 12 ~ www.njctl.org
Unit Review 1. a 2. d 3. dependent- height, independent- age 4. dependent- price, independent- weight 5. Answers may vary. Ex: y= 5x + 2 6. -7 7. - 4 3 8. $199.99 9. $29.99 10. The set equation has the largest slope. 11. a. number of days the car is rented b. price c. $115 d. $150 e. Day Cars R Us Car Mart 1 $249 $240 2 $348 $355 3 $447 $470 4 $546 $585 5 $645 $700 f. Your parents should choose Cars R Us because it is cheaper than Car Mart. 12. a. number of people attending the party b. price c. $7.50 d. $50 e. People Pool Water Park 5 $105 $122.50 10 $160 $160 15 $215 $197.50 20 $270 $235 25 $325 $272.50 f. You should choose the water park for your party because it is cheaper than the pool. NJ Center for Teaching and Learning ~ 13 ~ www.njctl.org