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Hrs worked pay 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!
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Unit 8: Day 1Direct and Inverse Variation
Definition…
Direct Variation: y varies directly as x This means as x increases, y __________ as x decreases, y __________
increases!decreases!
Hrs worked 5 11 14 17pay 30.00 66.00 84.00 102.00
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:
constantxy
xy
The constant is $6 per hour!
1. If y varies directly as x and y = 6 when x = 8, find y when x = 12.
constantxy
1286 y
Use the general equation for direct variation, set up a proportion and solve!
728 y y = 9
Cross-multiply!
Solve for y (divide both sides by 8)
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?
constantsF
32810 F
Use the general equation for direct variation, set up a proportion and solve!
3208 F F = 40 lbs
Cross-multiply!
Solve for F (divide both sides by 8)
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?
constanttd
t210
5175
Use the general equation for direct variation, set up a proportion and solve!
1050175 t t = 6 hrs
Cross-multiply!
Solve for t (divide both sides by 175)
Definition…
Inverse Variation: y varies inversely as x This means as x increases, y __________ as x decreases, y __________
decreases!increases!
Miles 18 20 30 60Gal of gas 10 9 6 3
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:
constant yx
xy
The constant is 180 miles!
4. If y varies inversely as x and y = 6 when x = 2, find x when y = 4.
constant yx
)4)(()6)(2( x
Use the general equation for inverse variation, set up an equation and solve!
x = 3
Solve for x (divide both sides by 4)
x412
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.
constantVP
)50)(()25)(100( V
Use the general equation for inverse variation, set up an equation and solve!
V = 50 in3
Solve for V (divide both sides by 50)
V502500
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.
constantnt
)12)(()15)(16( n
Use the general equation for inverse variation, set up an equation and solve!
n = 20 slices
Solve for n (divide both sides by 12)
n12240
