1. Unit 8: Day 1 Direct and Inverse Variation

2. Definition… Direct Variation: y varies directly as x This means as x increases, y __________ as x decreases, y __________ increases! decreases!

3. Hrs worked5111417 pay30.0066.0084.00102.00 How would you find the constant rate? Divide the pay by the hours worked! The more hours you work, the more you earn! General Equation for direct variation : x y The constant is $6 per hour!

4. 1. If y varies directly as x and y = 6 when x = 8, find y when x = 12. Use the general equation for direct variation, set up a proportion and solve! y = 9 Cross-multiply! Solve for y (divide both sides by 8)

5. 2. The force required to stretch a spring, F, varies directly with the amount the spring is stretched, s. Ten pounds is needed to stretch a spring 8 inches. How many pounds would be needed to stretch the spring 32 inches? Use the general equation for direct variation, set up a proportion and solve! F = 40 lbs Cross-multiply! Solve for F (divide both sides by 8)

6. 3. The distance, d, varies directly with the time, t. If you have driven 175 miles for 5 hours. How long would you drive for 210 miles? Use the general equation for direct variation, set up a proportion and solve! t = 6 hrs Cross-multiply! Solve for t (divide both sides by 175)

7. Definition… Inverse Variation: y varies inversely as x This means as x increases, y __________ as x decreases, y __________ decreases! increases!

8. Miles18203060 Gal of gas10963 How would you find the constant rate? Multiply miles and gallons! The more you drive, the less gas you have! General Equation for inverse variation : x y The constant is 180 miles!

9. 4. If y varies inversely as x and y = 6 when x = 2, find x when y = 4. Use the general equation for inverse variation, set up an equation and solve! x = 3 Solve for x (divide both sides by 4)

10. 5. The volume, V, of a gas at constant temperature varies inversely with the pressure, P. When the volume is 100 cubic inches, the pressure is 25 pounds. Find the volume when the pressure is 50 pounds. Use the general equation for inverse variation, set up an equation and solve! V = 50 in 3 Solve for V (divide both sides by 50)

11. 6. The number of slices, n, cut from a bread loaf of constant length varies inversely as the uniform thickness, t, of each slice. When there are 16 slices, each slice is 15mm thick. Find the number of slices when the thickness is 12mm. Use the general equation for inverse variation, set up an equation and solve! n = 20 slices Solve for n (divide both sides by 12)