1. Section 2.7 Proportions and Direct Variation

2. 2.7 Lecture Guide: Proportions and Direct Variation Objective: Use proportions to solve word problems.

3. Proportion Algebraically or Verbally This proportion is read “a is to b as c is to d.” The extremes are a and d, and the means are b and c. Numerical Example or

4. Solve the following proportions. 2. 1.

5. Solve the following proportions. 4. 3.

6. Solve the following proportions. 6. 5.

7. Solve the following proportions. 7.

8. Solve the following proportions. 8.

9. 9. A quality-control inspector found 5 defective computer chips in the 2500 that were tested. How many defective chips would be expected in a shipment of 100,000 chips?

10. 10. The FDA allows 13 insect heads for every 100 grams of fig paste used in fig cookies. How many insect heads would be allowed in 5000 grams of fig paste?

11. 11. On a drawing of a set of house plans 3 cm represents a distance of 15 ft. What distance corresponds to 7.5 cm on the house plans?

12. Objective: Solve problems involving direct variation. Direct Variation If x and y are real variables and k is a real constant, then: Verbally y varies directly as x with constant of variation k. Algebraically Example: Numerical Example Graphical Example

13. 12. If y varies directly as x and y is 3 when x is 4, find y when x is 24.

14. 13. If m varies directly as n and m is 12 when n is 5, find m when n is 60.

15. 14. The distance a plane travels varies directly with time. The plane travels 1275 miles in 3 hrs. (a) What is the constant of variation? (b) Use the constant of variation to write an equation relating the distance the plane travels to the time it takes to travel that distance.

16. 14. The distance a plane travels varies directly with time. The plane travels 1275 miles in 3 hrs. (c) Use this equation and a graphing calculator to complete the table of values shown below. Write the values from your table here. Time, xDistance, Y 1 0 1.5 3 4.5 6 7.5 9