1. 2.7 Variation

2. Direct Variation Let x and y denote 2 quantities. Then y varies directly with x, or y is directly proportional to x, if there is a nonzero number k such that y = kx The number k is called the constant of proportionality.

3. Inverse Variation Let x and y denote 2 quantities. Then y varies inversely with x, or y is inversely proportional to x, if there is a nonzero number k such that y = k / x

4. Joint Variation and Combined Variation When a variable quantity Q is proportional to the product of 2 or more other variables, we say that Q varies jointly with these quantities. Combinations of direct and / or inverse variation may occur. This is referred to as combined variation.

5. Write a general formula to describe each variation a varies directly with b; a = 24 when b = 6 m varies inversely with n squared; m = 2 and n = 3 z varies jointly with w and the square root of b; z = 18, w = 4, and b = 9 m varies directly with the square of b and inversely with the cube root of a; m = 4, b = 3, and a = 27

6. Solving Variation Problems 1.Express the variation algebraically 2.Use k for the constant of variation 3.Find k from the given information 4.Write the specific formula for the variation 5.Solve for the required unknown in the problem

7. Write a general formula and solve each variation problem Hooke’s Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 12 pounds stretches a certain spring 8 inches, how much will a force of 30 pounds stretch the string?

8. Write a general formula and solve each variation problem The illumination produced by a light source varies inversely as the square of the distance from the source. The illumination of a light source at 5 meters is 70 candela. What is the illumination 12 meters from the source?