1. Lesson 70: Solving Direct Variation Problems

2. Bell Work: Graph the points (-2, -4) and (6, 0) and draw a line through the points. Then write the equation of the line.

3. Answer: y = ½x – 3

4. Recall that quantities which vary directly are proportional. The table below shows that the total price of CDs varies directly with the number of CDs a customer purchases. # of CDsPrice ($) 115 230 345 460

5. The ratio of number of CDs to price is constant. We often use the letter k for the constant of proportionality. price = k number

6. Every price/number ratio in the table equals the constant, which is 15. 15/1 = 30/2 = 45/3 = 60/4= 15

7. One quantity (the price) is determined by multiplying the other variable (the number of CDs) by the constant. price = 15 x number

8. When you know that two quantities vary directly, knowing just one set of paired numbers allows us to solve for missing numbers in other pairs.

9. Example: The amount Ellen charges for banquet food varies directly as the number of people that attend. If Ellen charges $780 for 60 people, how much does she charge for 100 people?

10. Answer: k = price = charge = $780 number number 60 k = $13 charge = $13 x 100 = $1300

11. Example: Driving at a constant speed, the distance Maggie travels varies directly with the amount of time she drives. If Maggie drives 75 miles in one and one-half hours, how long does it take her to drive 100 miles?

12. Answer: k = distance = 75 = 50mph time 1.5 Distance = 50 x Time 100 = 50t = 2 hours

13. Practice: There were 23 people in line in front of Delia waiting to be helped. Three minutes later there were 18 people waiting in front of Delia. Predict how much longer Delia will wait to be helped.

14. Answer: 3 minutes = 0.6 min/person 5 people Wait = 0.6min/person x 18 people 10.8 min ≈ 11 minutes

15. HW: Lesson 70 #1-25