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4.6 Direct Variation
Learning Objective: F.IF.1
F.IF.7
NAME __________________________________
I will determine if a function is a direct variation function
I will graph a direct variation function
Do the following graphs show direct variation? Write yes or no for each.
1.
2.
yes or no
3.
yes or no
Graph each line and then determine if it has direct variation.
3
4. y = 2x + 0
5. y =
x–1
2
yes or no
yes or no
yes or no
6. y = x
yes or no
Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve.
7. If y = 45 when x = 15, find x when y = 15.
8. If y = –4 when x = 2, find y when x = –6.
9. If y = –9 when x = 3, find y when x = –5.
10. If y = 4 when x = 16, find y when x = 6.
Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve.
11. If y = 72 when x = 8, find x when y = 63.
12. If y = 2 when x = 4, find y when x = 10.
Write a direct variation equation that relates the variables.
13. The weight W of an object is 9.8m/s2 times the mass of the object m.
14. Music downloads are $0.99 per song. The total cost of d songs is T.
15. The circumference of a circle C is approximately 3.14 times the diameter d.
16. The distance a jet travels varies directly as the number of hours it flies. A jet traveled 3420 miles in
6 hours.
a) Find the constant of variation, k.
b) Write a direct variation equation for the distance d flown in time t.
c) Estimate how many hours it will take for an airliner to fly 6500 miles. Round to nearest tenth.
17. The total cost of tickets to a local concert varies directly as the number of tickets you buy. 4
tickets cost $72.
a) Find the constant of variation, k.
b) Write an equation to show this direct variation
c) Find the cost of 11 tickets.
Find the slope of each pair of points.
18. (7, 1) (5, –2)
Answers: 1) yes
13) w = 9.8m
19. (4, 2) (–3, 2)
3) no
5) no
15) C = 3.14d
7) k = 3, y = 3x, x = 5
17) a) k = $18 per ticket
9) k = –3, y = –3x, y = 15
b) y = 18x
c) $198
19) 0
11) k = 9, y = 9x, x = 7