Answer C. It must be straight and through Origin (0,0)

Transcription

1 STUDY GUIDE UNIT 2 You will need a straightedge for this assessment. 1. Which graph represents a proportional relationship? Answer C. It must be straight and through Origin (0,0) 2. The graph shows the cost C in dollars of w pounds of blueberries, a proportional relationship. Select all the true statements. A. 1 pound of blueberries costs $2.75. B pounds of blueberries cost $1. C. 5 pounds of blueberries cost $ D. 12 pounds of blueberries cost $33. E. The point (2,6) is on the graph of the proportional relationship. 1

2 Answers: A and D The unit rate is $2.75 per pound (16.50 divided by 6) A. Is the unit rate B. Incorrect has units backwards C. Incorrect 5 times 2 is 10 not 2.75 D. Double 6 and you get 12 and 33 or 12 time 2.75 is 33 E. (2,6) has a constant or relationship of times 3 not Andre rode his bike at a constant speed. He rode 1 mile in 8 minutes. Which of these equations represents the amount of time t (in minutes) that it takes him to ride a distance of d miles? A. t = 8d B. t = 1 8 d C. t = d + 7 D. t = d 7 Answer: A If he rode 1 mile in 8 minutes The rate is 8 minutes per mile Therefore you need to multiply the unit rate (8) by the miles to get the time. In this case the distance is your (x) and time is your (y) We do not add or subtract in proportional relationships 2

3 4. The two lines represent the amount of water, over time, in two tanks that are the same size. Which container is filling slower? Explain how you know. Answer line B. At any spot on time (x axis) if you go up to lines, line B is less water therefore it is getting less water in same amount of time. At any position aligned with y axis (Water) if you go across to lines, line A will be in less time, therefore it is getting more water in less time or line A is faster and B is filling slower. 3

4 5. The table shows the weights of apples at a grocery store. number of apples weight in kilograms Complete the table so that there is a proportional relationship between the number of apples and their weight. 6. The equation F = 9 C + 32 relates temperature measured in degrees Celsius, C, to 5 degrees Fahrenheit, F. Determine whether there is a proportional relationship between C and F. Explain or show your reasoning. It is not proportional because the equation includes addition. Example: If Celsius is 10 degrees If Celsius is 20 degrees 1.8 times 10 equals 18 then add 32 = 50 degrees F 1.8 rimes 20 equals 36 then add 32 = 68 degrees F 50 divided by 10 = 5 68 divided by 20 = 3.4 They are not the same means not proportional 4

5 7. A recipe for salad dressing calls for 3 tablespoons of oil for every 2 tablespoons of vinegar. The line represents the relationship between the amount of oil and the amount of vinegar needed to make salad dressing according to this recipe. The point (1,1.5) is on the line. A. Label the axes appropriately. X axis (bottom) should be Vinegar and Y axis (side) should be Oil B. Write an equation that represents the proportional relationship between oil and vinegar. Indicate the meaning of each variable. Y = KX so Oil = 1.5 times Vinegar O=1.5V C. Explain the meaning of the point (1,1.5) in terms of the situation. When there is 1 tbs of Oil you need 1.5 tbs of Vinegar 5

6 8. Jada earns twice as much money per hour as Diego. Diego earns twice as much money per hour as Lin. Select all the graphs that could represent how much Jada, Diego, and Lin earn for different amounts of time worked. A. D. B. E. C. Answers are B and C 6

7 9. Three runners are training for a marathon. One day, they all run about ten miles, each at their own constant speed. This graph shows how long, in minutes, it takes Runner #1 to run d miles. The equation that relates Runner #2 s distance (in miles) with time (in minutes) is t = 8.5d. Runner #3 s information is in the table: distance (miles) time (minutes) Which of the three runners has the fastest pace? Explain how you know. Runner #2 is the fastest at 8.5 minutes per mile Runner #3 is 18 divided by 2 or 9 minutes per mile Runner #1 is 10 minutes per mile y/x is 10 for any point 7