1. Warm Up Sketch the graph and identify the slope and y intercept: 1.X = 2 2.Y = 4 3.2x + 4y = 8 4.2Y + 2 = 4 + 6x

2. Direct and Indirect Variation I can solve for an unknown using direct and indirect variations.

3. Direct/Indirect Variation Variation will concern two variables; for example height and weight of a person, and how, when one of these changes, the other might be expected to change.

4. Direct Variation Direct variation exists if the two variables change in the same direction; i.e. if one increases, so does the other. Example, the amount of time studying for a test is a direct variation of your test grade

5. Indirect Variation Indirect variation exists if one going up causes the other to go down. Example: speed and time to do a particular journey; the higher the speed, the shorter the time.

6. Direct or Inverse?? Work with a partner. Discuss each description. Tell whether the two variables are examples of direct variation or inverse variation. a. You bring 200 cookies to a party. Let n represent the number of people at the party and c represent the number of cookies each person receives. b. You work at a restaurant for 20 hours. Let r represent your hourly pay rate and p represent the total amount you earn. c. You are going on a 240-mile trip. Let t represent the number of hours driving and s represent the speed of the car.

7. Direct Variation When x and y are directly proportional, dividing these variables will give a constant result called the constant of proportionality or k. We could also write this y = kx. Given the value of x, multiply this number by k to find the value of y.

8. Example of direct variation Given that y and x are directly proportional, and y = 2 when x = 5, find the value of when x = 15. We first find value of k, using y = kx 2 = k(5) K = 2/5 Y = (2/5) (15) Y = 6 Now use this constant value in the equation y=kx for situation when x = 15.

9. Direct Variation Practice y varies directly with x. If y = -4 when x = 2, find y when x = -6. Y = 12 y varies directly with x. If y = 15 when x = -18, find y when x = 1.6. y varies directly with x. If y = 75 when x =25, find x when y = 25. Y = -4/3 Y = 25/3

10. Example of Indirect Variation Example: If it takes 4 hours at an average speed of 90 km/hour to do a certain journey, how long would it take at 120 km/hour? Y = K/x

11. Indirect Variation Practice y varies inversely with x. If y = 40 when x = 16, find x when y = -5. X = -128 y varies inversely with x. If y = 7 when x = -4, find y when x = 5. Y = -28/5

12. Classify the following graphs as a) Direct b) Inverse c) Neither

13. Tell whether x and y show direct variation, inverse variation, or neither. Explain your reasoning. 1. y − 1 = 2x 2. (1/5)y = x 3. 2y = 1/x

14. Real World Examples The electric current I, is amperes, in a circuit varies directly as the voltage V. When 12 volts are applied, the current is 4 amperes. What is the current when 18 volts are applied? The volume V of gas varies inversely to the pressure P. The volume of a gas is 200 cm 3 under pressure of 32 kg/cm 2. What will be its volume under pressure of 40 kg/cm 2 ?