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4.6 Direct Variation

4.6 Direct Variation. Notation. Y varies directly as X y=kx k is constant of variation Y is proportional to X y=kx As one goes up, the other goes up. Example 1. Distance varies directly as time. A car travels 100 miles at a constant speed in 2 hours. D=kt 100=k(2) k=50 D=50t.

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4.6 Direct Variation

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  1. 4.6 Direct Variation

  2. Notation • Y varies directly as X • y=kx • k is constant of variation • Y is proportional to X • y=kx • As one goes up, the other goes up.

  3. Example 1 • Distance varies directly as time. A car travels 100 miles at a constant speed in 2 hours. • D=kt • 100=k(2) • k=50 • D=50t

  4. Example 2 • The charge(in dollars) to customers for electricity(in Kilowatt-hours) varies directly as the number of kilowatt-hours used. It costs $52 to use 800 kilowatt-hours. How much to use 1000 kilowatt-hours?

  5. The distance a body falls from rest varies directly as the square of the time it falls. If a skydiver falls 64ft in 2 sec, how far will she fall in 8 sec?

  6. Joint Variation • Y varies jointly as X and Z • y=kxz • The interest on a loan is given by I=prt. Here, for a given principal p, the interest earned I varies jointly as the interest rate r, and the time t. If an investment earns $100 interest at 5% for 2 yr, how much interest would the same principal earn at 4.5% for 3 yr?

  7. Homework Pg.235:9,10,13,14,21-24,29,30

  8. Inverse Variation • As one variable increases, the other decreases. • Y varies inversely as X

  9. Example 1 • Volume of gas varies inversely as the pressure. For a certain gas, the volume is 10 cm cubed when the pressure is 6 kg per cm squared. Find the volume when pressure is 12kg per cm squared.

  10. Combined Variation • Body mass index (BMI) varies directly as a person’s weight in pounds and inversely as the square of a person’s height in inches. A person who is 118lbs and has a height of 64 inches has a BMI of 20. Find the BMI of a person who has weight of 165lbs and height of 70inches.

  11. Homework Pg. 235: 1-8,11,12,25-28,31-34

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