Graphing Equations Chapter Test

1. Which line on the graph has a slope of 2/3? Graphing Equations Chapter Test A. Line A B. Line B C. Line C D. Line D 2. Which equation is represented on the graph? A. y = 4x 6 B. y = -4x 6 C. y = 4x +6 D. y = 6x +4

3. Find the slope of the line that has a y-intercept of 3 and contains the point (6,-3). Patti is tracking the price of gas over a 10 week period. See the graph below to answer questions 4 6. 4. What is the y-intercept in this problem? What does it mean in the context of this problem?

5. What is the rate of change between week 3 and week 6? 6. What is the rate of change between week 0 and Week 3? Explain what the rate of change means in the context of this problem. 7. What is the x intercept for the equation: 3x + 5y = 27? 8. Judy bought 10 shares of a stock on February 1, 2008 for $350. On October 1, 2008 she sold the stock for $210. Find Judy s average monthly rate of change on the stock. 9. Graph the following equation on the grid. Identify the slope and the y intercept. 2x +5y = -15 Slope = Y intercept =

10. Which equation is equivalent to: 4x +2y = -12 A. y = -2x 6 C. y = -4x - 12 B. y = 2x 6 D. y = -2x + 6 11. Identify the graph that represents the function: y = x+3 A. B. C. D. 12. Joe is traveling to his sister s house for Thanksgiving. He begins his drive at 3am. He drives 210 miles in 3 hours. He then stops for a half hour break and drives another 90 miles in the next 2 hours. His trip ends at 10 am after driving a total of 377.5 miles. Create a graph to illustrate this problem. What is Joe s average rate of change between 3 am and 6 am? If Joe s rate of change for the first three hours had remained constant throughout the entire trip, what time would he have arrived at his sister s house?

13. A final exam contains multiple choice questions that are worth 2 points and free response questions that are worth 3 points. The test is worth 60 points. The equation that represents x multiple choice questions and y free response questions is: 2x +3y = 60. Graph the equation on the grid. Let x = the number of multiple choice questions and y = the number of free response questions. If there are 15 multiple choice questions on the test, how many free response questions are on the test? Justify your answer. Identify one other possibility for the number of each question on the test: Justify your answer. There could be multiple choice and free response.

Graphing Equations Chapter Test Answer Key 1. Which line on the graph has a slope of 2/3? (1 Point) A. Line A A B. Line B C. Line C D. Line D **Note: You can eliminate C & D immediately because they have negative slopes. Then you only need to count the slope for A & B. 2. Which equation is represented on the graph? (1 Point) A. y = 4x 6 A B. y = -4x 6 C. y = 4x +6 D. y = 6x +4 **This is another problem where you can eliminate answers that don t make sense. You know the y intercept is -6, so C & D can be eliminated! The line is rising so the slope is positive. Therefore, B can also be eliminated!

3. Find the slope of the line that has a y-intercept of 3 and contains the point (6,-3). (2 points) Slope = rise from one point to the next run Slope = 1 = -1-1 Patti is tracking the price of gas over a 10 week period. See the graph below to answer questions 4 6. 4. What is the y-intercept in this problem? What does it mean in the context of this problem? (2 points) The y-intercept is 2.40. In this problem the y-intercept indicates that when Patti first began tracking gas prices (week 0), the price was $2.40. 5. What is the rate of change between week 3 and week 6? (2 Points) Ordered pairs: (3, 3.20) (6, 2.20) y 2 y 1 = 2.20 3.20 = -1 x 2 x 1 6 3 3 The rate of change between week 3 and 6 is -1/3. This means that the price of gas dropped about $0.33 each week.

6. What is the rate of change between week 0 and Week 3? Explain what the rate of change means in the context of this problem. (3 Points) Ordered pairs: (0, 2.40) (3, 3.20) y 2 y 1 = 3.20 2.40=.8 =.27 x 2 x 1 3 0 3 The rate of change between week 0 and 3 is.27. This means that the price of gas rose about $0.27 each week between weeks 0 and 3. 7. What is the x intercept for the equation: 3x + 5y = 27? (2 points) X intercept: Let y = 0 3x +5(0) = 27 3x = 27 x = 9 The x intercept is 9. 3x = 27 3 3 8. Judy bought 10 shares of a stock on February 1, 2008 for $350. On October 1, 2008 she sold the stock for $210. Find Judy s average monthly rate of change on the stock. (2 points) Ordered pairs: (2, 350) (10, 210) y 2 y 1 = 210 350 = -140 = -17.5 x 2 x 1 10-2 8 Feb is month 2 October is month 10 Judy s average monthly rate of change is -17.5. She lost 17.5 dollars per month while holding that stock. 9. Graph the following equation on the grid. Identify the slope and the y intercept. (3 points) 2x +5y = -15 I am going to rewrite it in slope intercept form: Slope = -2/5 2x -2x +5y = -15 2x 5y = -2x 15 Y intercept = -3 5y = -2x 15 5 5 5 y = -2/5x -3 10. Which equation is equivalent to: 4x +2y = -12 (1 point) A. y = -2x 6 C. y = -4x - 12 B. y = 2x 6 D. y = -2x + 6 4x 4x +2y = -12 4x 2y = -4x 12 2y = -4x 12 2 2 2 y = -2x -6

11. Identify the graph that represents the function: y = x+3 (1 point) A. B. C. D. You can eliminate answer B because it represents a negative absolute value, since it is upside down. We also know that the graph shifts up if there is a constant after the absolute value. Therefore, we ve narrowed it down to A or D. Since y = 0, which x value would make sense, -3 or 3? -3 + 3 = 0, so the correct answer is A. You can also make a table of value and see which graph has the same points as the table of values.

12. Joe is traveling to his sister s house for Thanksgiving. He begins his drive at 3am. He drives 210 miles in 3 hours. He then stops for a half hour break and drives another 90 miles in the next 2 hours. His trip ends at 10 am after driving a total of 377.5 miles. (4 points) Create a graph to illustrate this problem. (2/4 points) What is Joe s average rate of change between 3 am and 6 am? If Joe s rate of change for the first three hours had remained constant throughout the entire trip, what time would he have arrived at his sister s house? Rate of change = slope Two points: 3am (3, 0) 6am (6, 210) Slope = y 2 y 1 = 210-0 = 210 = 70 X 2 x 1 6 3 3 The rate of change between 3am and 6 am is 70. Therefore, Joe maintained a constant rate of 70 miles per hour during this three hour time period. If Joe had been able to maintain a constant rate of 70 miles per hour throughout his entire trip he would have arrived at his sister s house at 8:24 am. D= rt Distance = 377.5 miles Rate = 70 miles per hour Time =? 377.5 = 70t 377.5 = 70t 70 70 T = 5.4 (5 hours and 24 minutes) **.4 = 4/10 = 2/5. 2/5 of 60 minutes = 2/5 60 = 24 3 am plus 5 hours and 24 minutes = 8:24 am.

12. A final exam contains multiple choice questions that are worth 2 points and free response questions that are worth 3 points. The test is worth 60 points. The equation that represents x multiple choice questions and y free response questions is: 2x +3y = 60. (4 points) Graph the equation on the grid. Let x = the number of multiple choice questions and y = the number of free response questions. In order to graph the equation, we must find the x and y intercepts: 2x +3y = 60 X Intercept Y Intercept 2x +3(0) = 60 2(0) +3y = 60 2x = 60 3y = 60 2 2 3 3 x = 30 y = 20 X intercept = 30 Y intercept = 20 If there are 15 multiple choice questions on the test, how many free response questions are on the test? Justify your answer. Since we know there are 15 multiple choice questions, we can substitute 15 for x and solve for y. 2(15) + 3y = 60 30+3y = 60 30 30 +3y = 60 30 3y = 30 3y/3 = 30/3 Y= 10 If there are 15 multiple choice questions, then there are 10 free response questions. Justify: 2(15) + 3(10) = 60 30+30 = 60 Identify one other possibility for the number of each question on the test: Justify your answer. There could be multiple choice and free response. There could be 21 multiple choice and 6 free response. 2(21) + 3(6) = 60 42 + 18 = 60 60 = 60 This test is worth 28 points