Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

Transcription

1 3A Worksheet 3A Short Answer Find an equation for the line: 1. through (2, 6) and perpendicular to y = 5 4 x through ( 7, 4) and vertical. Determine whether y varies directly with x. If so, find the constant of variation k and write the equation. 3. x y A cannery processed 605 pounds of strawberries in 3.5 hours. The cannery processed 2100 pounds in 10 hours. a. Write a linear equation to model the weight of strawberries S processed in T hours. b. How many pounds of strawberries can be processed in 12 hours? 5. The distance traveled at a constant speed is directly proportional to the time of travel. If Olivia traveled 112 miles in 3.5 hours, how many miles will Olivia travel in 8.9 hours at the same constant speed? 6. Make a mapping diagram for the relation. {( 1, 3), (0, 1), (3, 1), (4, 6)} 7. Graph the set of data. Decide whether a linear model is reasonable. If so, draw a trend line and write its equation. {(1, 7), ( 2, 1), (3, 13), ( 4, 3), (0, 5)} Write in standard form an equation of the line passing through the given point with the given slope. 8. slope = 8; ( 2, 2) Determine whether y varies directly with x. If so, find the constant of variation k. 9. 8y = 7x 27 Find the value of y for a given value of x, if y varies directly with x. 10. If y = 4.8 when x = 2.4, what is y when x = 2.05?

2 11. If y = 166 when x = 83, what is y when x = 23? 12. A leaky valve on the water meter overcharges the residents for one gallon of water in every months. The overcharged amount w varies directly with time t. a. Find the equation that models this direct variation. b. How many months it will take for the residents to be overcharged for 8 gallons of water? Find the slope of the line. 15. A new candle is 8 inches tall and burns at a rate of 2 inches per hour. a. Write an equation that models the height h after t hours. b. Sketch the graph of the equation. 16. For,. 17. Suppose and. Find the value of. 18. Graph the equation. 19. The range of a car is the distance R in miles that a car can travel on a full tank of gas. The range varies directly with the capacity of the gas tank C in gallons. a. Find the constant of variation for a car whose range is 341 mi with a gas tank that holds 22 gal. b. Write an equation to model the relationship between the range and the capacity of the gas tank. Find the slope of the line through the pair of points. 20. ( 1 3, 0) and ( 1 2, 1 2 )

3 3A Worksheet 3A Answer Section SHORT ANSWER 1. ANS: y = 4 5 x 22 5 TOP: 2-2 Example 7 KEY: slope perpendicular equation of a line 2. ANS: x = 7 TOP: 2-2 Example 7 KEY: vertical line horizontal line equation of a line 3. ANS: yes; k = 1.2; y = 1.2x PTS: 1 DIF: L3 REF: 2-3 Direct Variation STA: ID M.03.a ID F.02.a ID PS.03 ID PS.04 TOP: 2-3 Example 1 KEY: constant of variation direct variation 4. ANS: S = 230T 200; 2560 lb PTS: 1 DIF: L2 REF: 2-4 Using Linear Models OBJ: Predicting With Linear Models STA: ID AL.01.a ID PS.03 ID PS.04 TOP: 2-4 Example 2 KEY: linear equation word problem problem solving multi-part question 5. ANS: mi STA: ID M.03.a ID F.02.a ID PS.03 ID PS.04 TOP: 2-3 Example 4 KEY: direct variation proportion problem solving word problem 6. ANS:

4 PTS: 1 DIF: L2 REF: 2-1 Relations and Functions OBJ: Graphing Relations STA: ID F.01 ID F.02 TOP: 2-1 Example 3 KEY: relation mapping diagram ordered pair 7. ANS: yes; y O x 4 PTS: 1 DIF: L3 REF: 2-4 Using Linear Models OBJ: Predicting With Linear Models STA: ID AL.01.a ID PS.03 ID PS.04 TOP: 2-4 Example 4 KEY: linear model trend line 8. ANS: 8x + y = 18 TOP: 2-2 Example 4 KEY: point-slope form standard form of linear equation 9. ANS: no STA: ID M.03.a ID F.02.a ID PS.03 ID PS.04 TOP: 2-3 Example 2 KEY: constant of variation

5 10. ANS: 4.1 STA: ID M.03.a ID F.02.a ID PS.03 ID PS.04 TOP: 2-3 Example 4 KEY: direct variation 11. ANS: 46 STA: ID M.03.a ID F.02.a ID PS.03 ID PS.04 TOP: 2-3 Example 4 KEY: direct variation 12. ANS: ; 20 months PTS: 1 DIF: L3 REF: 2-3 Direct Variation STA: ID M.03.a ID F.02.a ID PS.03 ID PS.04 TOP: 2-3 Example 3 KEY: constant of variation direct variation multi-part question problem solving word problem 13. ANS: 3 5 TOP: 2-2 Example 6 KEY: point-slope form standard form of linear equation slope 14. ANS: 1 2 TOP: 2-2 Example 6 KEY: slope 15. ANS:

6 15 t h PTS: 1 DIF: L2 REF: 2-4 Using Linear Models OBJ: Modeling Real-World Data STA: ID AL.01.a ID PS.03 ID PS.04 TOP: 2-4 Example 1 KEY: linear equation multi-part question 16. ANS: 19 PTS: 1 DIF: L2 REF: 2-1 Relations and Functions OBJ: Identifying Functions STA: ID F.01 ID F.02 TOP: 2-1 Example 6 KEY: function notation 17. ANS: PTS: 1 DIF: L3 REF: 2-1 Relations and Functions OBJ: Identifying Functions STA: ID F.01 ID F.02 TOP: 2-1 Example 6 KEY: function notation 18. ANS: y O 2 4 x 2 4 OBJ: Graphing Linear Equations STA: ID AL.01.a ID AL.03.a ID F.01.a TOP: 2-2 Example 1 KEY: linear equation graphing

7 19. ANS: mi/gal; R = C STA: ID M.03.a ID F.02.a ID PS.03 ID PS.04 TOP: 2-3 Example 3 KEY: constant of variation direct variation multi-part question word problem problem solving 20. ANS: 3 PTS: 1 DIF: L3 REF: 2-2 Linear Equations OBJ: Graphing Linear Equations STA: ID AL.01.a ID AL.03.a ID F.01.a TOP: 2-2 Example 3 KEY: slope