Review. Name: Class: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question.

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1 Name: Class: Date: ID: A Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which line segment has slope 7 4? i) ii) iii) iv) a. iii c. i b. ii d. iv. Determine the slope of the line that passes through G(3, 3) and H( 5, 9). a. 3 c. 3 b. 3 d. 3 1

2 Name: ID: A 3. Is the slope of this line segment positive, negative, zero, or not defined? a. negative c. positive b. not defined d. zero 4. A straight section of an Olympic downhill ski course is 34 m long. It drops 16 m in height. Determine the slope of this part of the course. a b c d A skateboard ramp rises ft. for every 7 ft. measured horizontally. What is the run? a. 7 c. b. 7 d Which of these line segments are parallel? a. CD and EF c. AB and CD b. EF and GH d. AB and EF

3 Name: ID: A 7. Determine the slope of the line that is perpendicular to this line segment. a. 3 c. 1 3 b. 3 d A line has x-intercept 4 and y-intercept 5. Determine the slope of a line perpendicular to this line. a. 4 5 c. 5 4 b. 5 4 d The slope of a line is 1. What is the slope of a line that is parallel to this line? 7 a. 7 c. b d The slope of a line is 1. What is the slope of a line that is perpendicular to this line? 7 a. 14 b. 7 d. c A line passes through J( 10, 10) and K(7, 9). Determine the coordinates of L so that line JL is perpendicular to line JK. a. L(7, 9) c. L(17, 19) b. L( 19, 17) d. L(9, 7) 3

4 Name: ID: A 1. A line passes through D( 5, 3) and N(1, 4). Determine the coordinates of two points on a line parallel to DN. a. (6, 10) and (4, 8) c. ( 10, 6) and (4, 8) b. ( 10, 4) and (6, 8) d. ( 10, 6) and ( 8, 4) 13. A line passes through R(8, 1) and F( 5, 4). Determine the coordinates of two points on a line perpendicular to RF. a. (16, 11) and (1, ) c. (16, ) and (1, 11) b. (, 16) and (1, 11) d. (16, ) and ( 11, 1) 14. Predict what will be common about the graphs of these equations. i) y = x 6 iii) y = 5x 6 ii) y = 3x 6 iv) y = 5x 6 a. All the graphs will have the same y-intercept. b. All the graphs will have the same x-intercept. c. All the graphs will have the same slope. d. None of the above. 4

5 Name: ID: A 15. Which graph represents the equation y = 5 x + 1? a. c. b. d. 5

6 Name: ID: A 16. Which graph has slope 1 and y-intercept 0? a. c. b. d. 6

7 Name: ID: A 17. Determine the slope and y-intercept of this graph. a. slope: 1 ; y-intercept: 1.5 c. slope: 1 ; y-intercept: 1.5 b. slope: 1 ; y-intercept: 1.5 d. slope: 1 ; y-intercept: Write an equation in slope-point form for this line. a. y = 1 (x ) c. y = 1 (x ) b. y + = 1 (x + ) d. y + = 1 (x + ) 19. Distance travelled, d, is a linear function of time, t. After 75 min. a bus travelled 50 km. After 165 min. the bus travelled 110 km. Write an equation to represent this function. a. d 50 = 3 (t 75) c. d 50 = 3 (t 75) b. d 50 = 3 (t 75) d. d 75 = (t 50) 3 7

8 Name: ID: A 0. Write an equation in slope-point form for the line that passes through A(, 4) and B( 9, 6). a. y 6 = 7 (x + ) c. y 4 = (x + ) 7 b. y + 4 = 7 (x ) d. y + 6 = (x ) 7 1. Write this equation in general form: y = 3x + 5 a. 3x + y 5 = 0 c. 3x y + 5 = 0 b. 3x + y + 5 = 0 d. 3x y 5 = 0. Which graph represents the equation 4x 5y 0 = 0? a. c. b. d. 3. Which equation is equivalent to x 3y 9 = 0? a. y = 3 x + 3 c. y + 1 = (x 3) 3 b. y + 1 = 3 (x 6) d. y 7 = (x 6) 3 8

9 Name: ID: A 4. Jon has x egg cartons that hold 1 eggs and y egg cartons that hold 18 eggs. He uses these cartons to store 7 eggs. Which equation represents the relation? a. 1x + 18y 7 = 0 c. 1x 18y 7 = 0 b. 1x 18y + 7 = 0 d. 1x + 18y + 7 = 0 Short Answer 5. Describe the graph of the linear function whose equation is y = 3x i) Determine the slope and y-intercept of this graph. ii) Write an equation to describe the graph. 9

10 Name: ID: A 7. Write an equation in slope-point form for this line. 8. From January 010 to August 010, the amount of money in Shannon s savings account increased by $75 per month. In May 010, there was approximately $534 in her savings account. Write an equation in slope-point form to represent the amount of money in her savings account, s, as a function of the number of months, n, since December Write an equation for the line that passes through E( 3, 7) and F(, 10). Write the equation in slope-point form and in slope-intercept form. 30. Write this equation in general form: y 5 = 3 (x + 5) 5 10

11 Name: ID: A 31. a) Determine the x- and y-intercepts of the graph of this equation: 5x + 8y + 40 = 0 b) Graph the equation. Problem 3. Determine the slope of each line segment. 33. Construction workers are paving a road. The road must drop 4 cm for every 650 cm measured horizontally. a) What is the slope of the road? b) Suppose a section of the road drops 4.5 cm. How long is this section of the road measured horizontally? 11

12 Name: ID: A 34. A student said that the equation of this graph is y = 3 x. a) What mistakes did the student make? b) What is the equation of the graph? 35. Write an equation to describe this function. Verify the equation. 1

13 Name: ID: A 36. Students at Tahayghen Secondary School sell punch during the school carnival. The number of cups sold, n, is a linear function of the temperature in degrees Celsius, t. The students sold 458 cups when the temperature was 5 C. They sold 534 cups when the temperature was 9 C. a) Write an equation in slope-point form to represent this function. b) Use the equation in part a to determine the approximate temperature when the students sell 35 cups of punch. 37. Charles s Gas Law states that the volume, v, of a fixed mass of gas at a constant pressure varies directly with its absolute temperature, t. At 7 C, the volume of a certain amount of air is 500 ml. When the air is heated to 90 C, the volume increases to 605 ml. a) Write an equation in general form for this relation. b) Determine the volume of the air when its temperature is 60 C. c) Determine the temperature of the air when its volume is 1010 ml. 13

14 ID: A Review Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 DIF: Easy REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge. ANS: D PTS: 1 DIF: Easy REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge 3. ANS: A PTS: 1 DIF: Easy REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Conceptual Understanding 4. ANS: B PTS: 1 DIF: Moderate REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge 5. ANS: B PTS: 1 DIF: Easy REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge 6. ANS: D PTS: 1 DIF: Easy REF: 6. Slopes of Parallel and Perpendicular Lines LOC: 10.RF3 TOP: Relations and Functions KEY: Procedural Knowledge 7. ANS: D PTS: 1 DIF: Easy REF: 6. Slopes of Parallel and Perpendicular Lines LOC: 10.RF3 TOP: Relations and Functions KEY: Procedural Knowledge 8. ANS: A PTS: 1 DIF: Easy REF: 6. Slopes of Parallel and Perpendicular Lines LOC: 10.RF3 TOP: Relations and Functions KEY: Procedural Knowledge 9. ANS: C PTS: 1 DIF: Easy REF: 6. Slopes of Parallel and Perpendicular Lines LOC: 10.RF3 TOP: Relations and Functions KEY: Conceptual Understanding 10. ANS: A PTS: 1 DIF: Easy REF: 6. Slopes of Parallel and Perpendicular Lines LOC: 10.RF3 TOP: Relations and Functions KEY: Conceptual Understanding 11. ANS: D PTS: 1 DIF: Moderate REF: 6. Slopes of Parallel and Perpendicular Lines LOC: 10.RF3 TOP: Relations and Functions KEY: Procedural Knowledge 1. ANS: C PTS: 1 DIF: Moderate REF: 6. Slopes of Parallel and Perpendicular Lines LOC: 10.RF3 TOP: Relations and Functions KEY: Procedural Knowledge 13. ANS: C PTS: 1 DIF: Moderate REF: 6. Slopes of Parallel and Perpendicular Lines LOC: 10.RF3 TOP: Relations and Functions KEY: Procedural Knowledge 14. ANS: A PTS: 1 DIF: Easy REF: 6.3 Investigating Graphs of Linear Functions LOC: 10.RF7 TOP: Relations and Functions KEY: Conceptual Understanding 15. ANS: B PTS: 1 DIF: Easy REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function LOC: 10.RF7 TOP: Relations and Functions KEY: Conceptual Understanding 1

15 ID: A 16. ANS: B PTS: 1 DIF: Easy REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function LOC: 10.RF7 TOP: Relations and Functions KEY: Conceptual Understanding 17. ANS: A PTS: 1 DIF: Easy REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function LOC: 10.RF7 TOP: Relations and Functions KEY: Conceptual Understanding 18. ANS: A PTS: 1 DIF: Easy REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding 19. ANS: A PTS: 1 DIF: Easy REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge 0. ANS: C PTS: 1 DIF: Easy REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge 1. ANS: C PTS: 1 DIF: Easy REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding. ANS: C PTS: 1 DIF: Easy REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge 3. ANS: C PTS: 1 DIF: Moderate REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding 4. ANS: A PTS: 1 DIF: Moderate REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding SHORT ANSWER 5. ANS: The graph has a slope of 3 and a y-intercept of 3. PTS: 1 DIF: Easy REF: 6.3 Investigating Graphs of Linear Functions LOC: 10.RF7 TOP: Relations and Functions KEY: Conceptual Understanding

16 ID: A 6. ANS: i) slope: 1 ; y-intercept: 3 ii) y = 1 3 x PTS: 1 DIF: Moderate REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding 7. ANS: y 7 = 7 (x + 4) PTS: 1 DIF: Moderate REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF7 TOP: Relations and Functions KEY: Conceptual Understanding 8. ANS: s 534 = 75(n 5) PTS: 1 DIF: Moderate REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF7 TOP: Relations and Functions KEY: Conceptual Understanding 9. ANS: y + 7 = 17 (x + 3) 5 y = 17 5 x or y 10 = 17 (x ) 5 y = 17 5 x PTS: 1 DIF: Moderate REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF7 TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge 30. ANS: 3x 5y + 40 = 0 PTS: 1 DIF: Easy REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding 3

17 ID: A 31. ANS: a) x-intercept: 8 y-intercept: 5 b) PTS: 1 DIF: Moderate REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6 TOP: Relations and Functions KEY: Conceptual Understanding Procedural Knowledge 4

18 ID: A PROBLEM 3. ANS: Count units to determine the rise and run. From R to Q, both x and y are increasing, so the rise is 4 and the run is 6. Slope = rise run Slope = 4 6 Slope = 3 Line segment RQ has slope 3. From R to S, y is decreasing, so the rise is 3; x is increasing, so the run is 5. Slope = rise run Slope = 3 5 Slope = 3 5 Line segment RS has slope 3 5. From S to Q, both x and y are increasing, so the rise is 7 and the run is 1. Slope = rise run Slope = 7 1 Line segment SQ has slope 7. PTS: 1 DIF: Moderate REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Problem-Solving Skills 5

19 ID: A 33. ANS: a) Slope = rise run Slope = Slope = 35 The slope of the road is 35. b) The distance the road drops is the rise. Since the road drops, the rise is negative. The section of the road measured horizontally is the run. Slope = rise run 35 = 4.5 run Ê ˆ Ê 4.5 ˆ runá = run Ë 35 Á Ë run ( run) = Ê ( run) ˆ 35Á = (35)( 4.5) Ë 35 ( ) run = (35)( 4.5) ( ) run = 7963 run = The section of the road measured horizontally is cm long. PTS: 1 DIF: Moderate REF: 6.1 Slope of a Line LOC: 10.RF5 TOP: Relations and Functions KEY: Communication Problem-Solving Skills 6

20 ID: A 34. ANS: a) The student may have interchanged the signs of the slope and y-intercept. b) Use the equation: y = mx + b To write the equation of a linear function, determine the slope of the line, m, and its y-intercept, b. The line intersects the y-axis at ; so, b =. From the graph, the rise is 3 when the run is. So, m = 3, or m = 3 Substitute for m and b in y = mx + b. y = 3 x + The equation of the graph is: y = 3 x + PTS: 1 DIF: Moderate REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Communication Problem-Solving Skills 7

21 ID: A 35. ANS: Use the equation: y = mx + b To write the equation of a linear function, determine the slope of the line, m, and its y-intercept, b. The line intersects the y-axis at 3; so, b = 3. From the graph, the rise is 4 when the run is 5. So, m = 4 5 Substitute for m and b in y = mx + b. y = 4 5 x 3 An equation for the function is: y = 4 5 x 3 To verify the equation, substitute the coordinates of a point on the line into the equation. Choose the point (0, 3). Substitute x = 0 and y = 3 into the equation: y = 4 5 x 3 L.S. = y = 3 R.S. = 4 5 x 3 = 4 5 (0) 3 = 3 Since the left side is equal to the right side, the equation is correct. PTS: 1 DIF: Moderate REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function LOC: 10.RF6 TOP: Relations and Functions KEY: Communication Problem-Solving Skills 8

22 ID: A 36. ANS: a) n = f(t), so two points on the graph have coordinates C(5, 458) and D(9, 534). Use this form for the equation of a linear function: n n 1 t t 1 = n n 1 t t 1 Substitute: n 1 = 458, t 1 = 5, n = 534, and t = 9 n 458 t 5 n 458 t 5 = 19 = Ê n 458 ˆ ( t 5) Á = 19 ( t 5) Ë t 5 n 458 = 19 ( t 5) In slope-point form, the equation that represents this function is: n 458 = 19 ( t 5) b) Use: n 458 = 19 ( t 5) Substitute: n = 35 n 458 = 19 ( t 5) = 19 ( t 5) 133 = 19t = 19t t = 18 When the students sell 35 cups of punch, the approximate temperature is 18 C. PTS: 1 DIF: Difficult REF: 6.5 Slope-Point Form of the Equation for a Linear Function LOC: 10.RF7 TOP: Relations and Functions KEY: Problem-Solving Skills 9

23 ID: A 37. ANS: a) v = f(t), so two points on the graph have coordinates A(7, 500) and B(90, 605). Use this form for the equation of a linear function: v v 1 t t 1 = v v 1 t t 1 Substitute: t 1 = 7, v 1 = 500, t = 90, and v = 605 Ê ( t 7) Á Ë v 500 t 7 = v 500 t 7 = v 500 t 7 = 5 3 v 500 t 7 ˆ v 500 = (3)( v 500) = = 5 3 ( t 7) 5t Ê Á Ë 5t v 1500 = 5t 135 ˆ (3) 0 = 5t 3v = 5t 3v In general form, the equation that represents this function is: 5t 3v = 0 b) Use: 5t 3v = 0 Substitute: t = 60 5t 3v = 0 5(60) 3v = v = = 3v 1665 = 3v v = 555 When the temperature of the air is 60 C, its volume is 555 ml. c) Use: 10

24 ID: A 5t 3v = 0 Substitute: v = t 3v = 0 5t 3(1010) = 0 5t = = 5t 1665 = 5t t = 333 When the volume of the air is 1010 ml, its temperature is 333 C. PTS: 1 DIF: Difficult REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF7 10.RF5 TOP: Relations and Functions KEY: Problem-Solving Skills 11