Lesson 8 Finding direct variation Direct variation When
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Lesson 8 Finding direct variation
Direct variation • When the statement of a problem says that A varies directly as B or that A is directly proportional to B, the equation • A = k. B is implied. • This is called a direct variation. • k is a constant in the equation and is called the constant of variation.
Examples of direct variation • -the circumference of a circle varies directly as the radius C = k. R • -the resistance is directly proportional to the length R = k. L • -the water produced varied directly as the amount of hydrogen burned • W = k. Hb
Solving direct variation problems • The number of seconds varies directly as the number of minutes. When 120 seconds have passed, 2 minutes have passed. If 300 seconds have passed, how many minutes have passed? • S = k. M • 120 =k 2 • K= 60 • S = 60 M • 300= 60 M • M=5
Fractional constant • Distance traveled is directly proportional to the time spent traveling. A motorized scooter can travel 10 kilometers in 30 minutes. How far can the scooter travel in 45 minutes? • D = k. T • 10=k 30 • K= 1/3 • D= 1/3 T • D = 1/3(45) = 15
Direct variation as a ratio • Another way to work direct variation problems is with a proportion • A 1 = B 1 • A 2 B 2 so A 1 B 2=A 2 B 1 • Cost varies directly as the number purchased. If 12 items can be purchased for $78, how much will 42 items cost • C 1 = N 1 78 = 12 • C 2 N 2 C 2 42 • 78(42) = 12 C 2 • 273 = C 2
examples • 1) Sale price varies directly as the original price. If a shirt normally priced T $30 is on sale for $21, what is the sale price of a shirt normally priced at $40? • 2) The perimeter of a square varies directly as the length of one side. If the perimeter is 20 when the side is 5, what is the perimeter when the side is 9?
